RILEY, Chief Judge.
Marquise Laguan Bowie, Joe Darrell Edwards, Jr., and ten other members of the Minneapolis, Minnesota gang, the Rolling Thirties Bloods (RTB), were indicted on federal drug and firearms charges. Bowie pled guilty to conspiracy to distribute and possess with intent to distribute 50 grams or more of crack cocaine, and the district court2 sentenced Bowie to 175 months imprisonment. After a bench trial, the district court found Edwards guilty of conspiracy to distribute and possess with intent to distribute 50 grams or more of crack cocaine and conspiracy to possess firearms during and in relation to a drug trafficking crime, and sentenced Edwards to 206 months imprisonment. Bowie and Edwards challenge their convictions and sentences on various grounds. We affirm.
1. BACKGROUND
On August 22, 2007, a grand jury returned a forty count indictment against Bowie, Edwards, and other RTB gang members. Count 1 of the indictment charged each of the co-defendants with conspiracy to distribute and possess with intent to distribute 50 grams or more of crack cocaine from 1990 through August 2007, in violation of 21 U.S.C. §§ 841(a)(1) and (b)(1)(A), and 846; Count 2 of the indictment charged each of the co-defendants with conspiracy to possess firearms during and in relation to a drug trafficking crime from 1990 to August 2007, in violation of 18 U.S.C. § 924(o). The indictment also charged Bowie with two counts, and Edwards with one count, of aiding and abetting distribution of crack cocaine, in violation of 21 U.S.C. § 841(a)(1) and (b)(1)(C), and 18 U.S.C. § 2.
A. Bowie
On February 1, 2008, Bowie pled guilty to Count 1 of the indictment pursuant to a written plea agreement. The district court found Bowie entered the plea knowingly and voluntarily and accepted Bowie’s guilty plea. Over a year later, on February 13, 2009, Bowie filed pro se motions to withdraw his guilty plea and fire his attorney for ineffective assistance of counsel. [809]*809Bowie’s counsel did not join Bowie’s pro se motions. Bowie claimed (1) he was not aware of the full nature of the plea agreement; (2) his attorney failed to explain the plea agreement line by line; (3) the plea agreement did not provide an accurate portrayal of Bowie’s role in the conspiracy; (4) Bowie only signed the agreement at the direction of his attorney; (5) Bowie’s attorney failed to object to any portion of the plea agreement; (6) Bowie’s attorney did not advise him of the applicable United States Sentencing Guidelines (Guidelines or U.S.S.G.) provisions; (7) Bowie requested, but never received, a copy of the indictment, a bill of particulars, and other documents; and (8) Bowie believed the indictment was based on false testimony.
The district court convened a hearing to address Bowie’s motions. After hearing from Bowie, Bowie’s attorney, and the government, the district court determined there was “no fair and just reason to grant withdrawal of the plea at this time,” and denied Bowie’s motion to fire his attorney.
In March 2009, the district court sentenced Bowie. Bowie moved for a downward variance based on the sentencing disparity between crack cocaine and powder cocaine offenses and the resulting racial impact, and the parties addressed this issue at the sentencing hearing. Although the district court did not vary downward based on the crack versus powder cocaine ratio, the court gave credit to Bowie for time served and sentenced him to 175 months imprisonment.
B. Edwards
Edwards pled not guilty to the charges against him and filed various motions, including a motion for a bill of particulars and a motion to dismiss the charges against him, which the district court denied. Befoi’e trial, Edwards filed additional motions, including a motion to compel the government to disclose certain witness statements and a motion to dismiss the indictment. The district court granted in part, and denied in part, Edwards’s motion for disclosure of witness statements, and denied the motion to dismiss the indictment.
After Edwards waived his right to a jury trial, the district court presided over a bench trial in July and August of 2008. In September 2008, the district cour found Edwards guilty of the crack cocaine and firearms conspiracies charged in Counts 1 and 2 of the indictment and not guilty of the charge of aiding and abetting distribution of crack cocaine. Edwards filed a motion for a judgment of acquittal, a new trial, or to re-open, which the district court denied in its entirety. The district court initially sentenced Edwards to two concurrent terms of 216 months imprisonment but later reduced the terms of imprisonment to 206 months to give Edwards credit for time served.
II. DISCUSSION
A. Bowie’s Arguments
Bowie challenges his conviction and sentence, arguing the district court (1) failed to establish a factual basis for Bowie’s guilty plea, (2) erred in denying Bowie’s motion to withdraw his guilty plea, and (3) erroneously refused to consider the crack versus powder cocaine sentencing disparity in fashioning Bowie’s sentence.
1. Factual Basis for Guilty Plea
Bowie first contends his guilty plea had an insufficient factual basis. Bowie insists, because the case involved a complex conspiracy over a seventeen year period, the district court’s paraphrasing of the plea agreement was insufficient to establish a factual basis for the plea. We disagree.
[810]*810Under Fed.R.Crim.P. 11(b)(3), “[b]efore entering judgment on a guilty plea, the court must determine that there is a factual basis for the plea.” “A guilty plea is supported by an adequate factual basis when the record contains ‘sufficient evidence at the time of the plea upon which a court may reasonably determine that the defendant likely committed the offense.’ ” United States v. Cheney, 571 F.3d 764, 769 (8th Cir.2009) (quoting United States v. Gamble, 327 F.3d 662, 664 (8th Cir.2003)). “We have held that facts gathered from the prosecutor’s summarization of the plea agreement and the language of the plea agreement itself, a colloquy between the defendant and the district court, and the stipulated facts before the district court, are sufficient to find a factual basis for a guilty plea.” United States v. Brown, 331 F.3d 591, 595 (8th Cir.2003) (internal citations omitted).
The transcript of Bowie’s plea hearing reveals the district court had sufficient information to reasonably determine Bowie likely committed the offense. The district court stated,
I will go back to the first page of the agreement called the factual basis....
It states that you agree that from at least 1998 through October of 2007, here in Minnesota, that you did knowingly and intentionally, conspir[e] with other people ... to possess with intent to distribute and to distribute more than 50 grams of crack cocaine. Is that true, sir?
Bowie responded, “Yes, sir.” Bowie also agreed the conspiracy involved more than 1.5, but less than 4.5, kilograms of crack cocaine. Bowie unequivocally admitted he participated in the crack cocaine distribution conspiracy, both in writing and at the plea hearing. In addition, Bowie admitted to the probation officer who prepared his presentence investigation report “that he distributed up to an ‘eight-ball’ of cocaine base per week” from the age of seventeen to twenty-five. We conclude the district court adequately established a factual basis for Bowie’s guilty plea before entering judgment.
2. Motion to Withdraw Guilty Plea
Next, Bowie argues the district court erred in denying Bowie’s motion to withdraw his guilty plea. We review a district court’s denial of a motion to withdraw a guilty plea for abuse of discretion. See United States v. Davis, 583 F.3d 1081, 1089 (8th Cir.2009). “A defendant may withdraw a plea of guilty ... after the court accepts the plea, but before it imposes sentence if ... the defendant can show a fair and just reason for requesting the withdrawal.” Fed.R.Crim.P. 11(d)(2)(B). “In addition to a ‘fair and just reason’ for withdrawal, a district court may consider whether the defendant asserts his legal innocence to the charge, the length of time between the guilty plea and the motion to withdraw, and whether the withdrawal would prejudice the government.” United States v. Teeter, 561 F.3d 768, 770 (8th Cir.2009). “ ‘A guilty plea is a solemn act not to be set aside lightly.’ ” Davis, 583 F.3d at 1089 (quoting United States v. Prior, 107 F.3d 654, 657 (8th Cir.1997)).
On appeal, Bowie claims he should have been allowed to withdraw his guilty plea because he did not understand the conspiracy charge to which he pled guilty. However, at the plea hearing, Bowie confirmed (1) no one had threatened him or forced him to sign the plea agreement; (2) he understood he was pleading guilty to Count I of the indictment; (3) he was aware there was a statutory mandatory minimum of ten years imprisonment and a maximum of life imprisonment for the offense described in Count I; (4) he agreed the conspiracy involved more than [811]*8111.5 kilograms, but less than 4.5 kilograms, of crack cocaine; (5) he was aware his offense level and criminal history category would determine his Guidelines range; and (6) he understood that once he entered a guilty plea, it would be “very difficult ... to back out of the agreement.” Like the district court, we conclude Bowie failed to show a fair and just reason for his request to withdraw his guilty plea more than one year after he entered the plea. “ ‘Post-plea regrets by a defendant caused by contemplation of the prison term he faces are not a fair and just reason for a district court to allow a defendant to withdraw a guilty plea, or for this court to reverse the district court.’ ” Id. (quoting Teeter, 561 F.3d at 770-71).
3. Bowie’s Sentence
Lastly, Bowie maintains the district court erred in refusing to consider the sentencing disparity between crack cocaine and powder cocaine offenses in fashioning Bowie’s sentence. We review the sentence imposed by a district court for an abuse of discretion. See United States v. Lomeli, 596 F.3d 496, 503 (8th Cir.2010). In so doing, we “giv[e] due deference to the district court’s decision.” Id. (quoting United States v. Braggs, 511 F.3d 808, 812 (8th Cir.2008)). We must first “ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range, treating the Guidelines as mandatory, failing to consider the [18 U.S.C.] § 3553(a) factors, selecting a sentence based on clearly erroneous facts, or failing to adequately explain the chosen sentence.” Id. (quoting Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007)). If we determine the district court did not commit procedural error, we then consider the substantive reasonableness of the sentence. See id.
Bowie insists his sentence should be vacated because the record is silent as to whether the district court was aware of its authority to consider the crack versus powder cocaine sentencing disparity in sentencing Bowie. We disagree. Although it would have been preferable for the district court to address explicitly Bowie’s motion for a downward variance based on the sentencing disparity, we find no error in the district court’s failure to do so. In United States v. Boyce, 564 F.3d 911, 917 (8th Cir.2009), we held “[t]he district court need not respond to every argument advanced by a defendant,” and where “[b]oth [counsel for the defendant] and the government commented on the district court’s discretion to consider this disparity, ... we may presume the district court was aware of this policy guidance.” Furthermore, “[w]hile the district court would have been within its discretion to consider the crack versus powder cocaine disparity in sentencing [Bowie], the district court certainly was not required to vary downward on this basis.” Davis, 583 F.3d at 1099. The district court committed no procedural error and Bowie’s sentence is not substantively unreasonable. We affirm the district court’s judgment with respect to Bowie.
B. Edwards’s Arguments on Appeal
We next consider Edwards’s appeal. Edwards challenges his conviction and sentence on various grounds, arguing (1) the evidence at trial was insufficient to support his conviction; (2) the district court admitted improper evidence at trial; (3) prosecutorial misconduct deprived him of a fair trial; (4) the district court was biased against him, which prejudiced the verdict; (5) the district court erred in denying him a bill of particulars; (6) the district court erred in denying his motion to dismiss the indictment; (7) the district [812]*812court erred in failing to order disclosure of exculpatory evidence; and (8) the district court abused its discretion in sentencing him.
1. Sufficiency of the Evidence
Edwards first claims the government failed to present sufficient evidence to support the district court’s findings beyond a reasonable doubt that Edwards participated in the crack cocaine and firearms conspiracies. Edwards insists his convictions were based solely on irrelevant RTB gang evidence, and vague and incredible testimony from RTB members seeking lower sentences.
“In reviewing the sufficiency of the evidence after a bench trial, we apply the same standard that we apply when reviewing a jury verdict.” United States v. Vaughn, 410 F.3d 1002, 1004 (8th Cir.2005). “ ‘We review the sufficiency of the evidence de novo, viewing evidence in the light most favorable to the government, resolving conflicts in the government’s favor, and accepting all reasonable inferences that support the verdict.’ ” United States v. Lockett, 601 F.3d 837, 840 (8th Cir.2010) (quoting United States v. Washington, 318 F.3d 845, 852 (8th Cir.2003)). “When considering a challenge to a conspiracy conviction based upon sufficiency of the evidence, ‘we will affirm if the record, viewed most favorably to the government, contains substantial evidence supporting the jury’s verdict, which means evidence sufficient to prove the elements of the crime beyond a reasonable doubt.’ ” United States v. Hodge, 594 F.3d 614, 617 (8th Cir.2010) (quoting United States v. Lopez, 443 F.3d 1026, 1030 (8th Cir.2006) (en banc)). A verdict will only be overturned “if no reasonable jury could have found [the defendant] guilty beyond a reasonable doubt.” United States v. Gray, 369 F.3d 1024, 1028 (8th Cir.2004).
“To establish that a defendant conspired to distribute drugs under 21 U.S.C. § 846, the government must prove: (1) that there was a conspiracy, i.e., an agreement to distribute the drugs; (2) that the defendant knew of the conspiracy; and (3) that the defendant intentionally joined the conspiracy.” United States v. Hernandez, 569 F.3d 893, 896 (8th Cir.2009) (quoting United States v. Jiminez, 487 F.3d 1140, 1146 (8th Cir.2007)). “To establish that a defendant conspired to use, carry or possess a firearm in violation of [18 U.S.C.] § 924(c) and (o), the Government must prove: (1) that there was a conspiracy, i.e., an agreement either to use or carry a firearm during and in relation to a drug trafficking crime or to possess a firearm in furtherance of a drug trafficking crime; (2) that the defendant knew of the conspiracy; and (3) that the defendant intentionally joined the conspiracy.” United States v. Saddler, 538 F.3d 879, 889 (8th Cir.2008). “A formal agreement is not required to create a conspiracy, and the existence of a conspiracy can be proved by direct or circumstantial evidence.” United States v. Williams, 534 F.3d 980, 985 (8th Cir.2008).
The district court issued a thirty-four page memorandum with findings of fact and conclusions of law, finding Edwards guilty of both the crack cocaine and firearms conspiracies. The district court found Edwards joined the RTB in 1983 when he was approximately 12 years old, and he held the status of an “Original Blood” or an “Original Gangster,” meaning he was an older, generally more respected member of the gang. The court heard evidence that RTB members “who seriously identify with the gang’s values and rules” were called “riders.” While incarcerated, Edwards wrote letters indicating Edwards viewed himself as a rider. The district court determined the RTB gang [813]*813members “established themselves as the exclusive crack cocaine dealers within their territory” in South Minneapolis. The court heard testimony there was an agreement and understanding among RTB members to sell drugs in their territory and ensure the territory was protected from rival gangs. The district court found the RTB members possessed and used firearms to facilitate drug transactions and to protect their territory.
The district court specifically found credible testimony that Edwards was a part of the agreement or understanding among the RTB members and Edwards personally possessed and sold crack cocaine and possessed firearms in connection with his RTB gang activities. In finding Edwards guilty of the conspiracy charges, the district court clarified,
The Court does not base its findings upon [Edwards’s] membership in or association with a particular group. The Court’s findings are based on evidence that [Edwards] was a participant in an agreement or understanding among the members of [RTB] to control their territory for the exclusive sale of crack cocaine, using and through the possession of firearms, and [Edwards’s] knowing support for, and activities in furtherance of, that agreement.
On appeal, Edwards relies largely on the fact he was imprisoned during the vast majority of the alleged seventeen-year conspiracy to support his argument that there is insufficient evidence to support his convictions. “In order to withdraw from a conspiracy, a defendant ‘must demonstrate that he took affirmative action to withdraw from the conspiracy by making a clean breast to the authorities or by communicating his withdrawal in a manner reasonably calculated to reach his eoconspirators.’ ” United States v. Jackson, 345 F.3d 638, 648 (8th Cir.2003) (quoting United States v. Zimmer, 299 F.3d 710, 718 (8th Cir.2002)). “A cessation of activities, alone, is not sufficient to establish a withdrawal from the conspiracy.” Id. The district court acknowledged Edwards was incarcerated for a large portion of the alleged conspiracy; however, the court found Edwards maintained his gang membership and continued to support the gang’s goals while in prison. The district court further found Edwards never “took any affirmative steps to withdraw from the conspiracy during the time he was incarcerated or at any other time.” The district court’s findings that Edwards’s activities while in prison and during the short periods of time he was out of jail were inconsistent with withdrawal are supported by sufficient evidence in the record and are reasonable.
Next Edwards suggests his conviction cannot stand because he was convicted based upon guilt by association. Edwards concedes the government may have demonstrated other RTB members were involved in drug distribution, but he insists the government did not present sufficient evidence to prove Edwards was involved in the drug trafficking and firearms conspiracies. Edwards insists the only evidence tying him to drug trafficking and firearm activity is vague, uncorroborated testimony from cooperating witnesses, and Edwards goes to great lengths to discredit the cooperating witnesses’ testimony.
Four RTB members testified against Edwards. Soloman Shannon and Calvin Ferguson each testified they personally observed Edwards sell crack cocaine and possess or talk about possessing a firearm. George Dixon and Jomoy Lee both reported they provided Edwards with crack cocaine, knowing Edwards intended to sell it. The district court acknowledged these four witnesses “could not identify the specific date or dates on which they gave or sold [814]*814drugs to [Edwards] or saw [Edwards] selling drugs,” but the district court explained this was not surprising because “individual instances of drug sales would not be an especially memorable event” for an RTB member. The district court also observed, “it seems likely ... that if the gang members were making up evidence against [Edwards], they would have said things that were more incriminating for [Edwards].”
“It is well-established that ‘the uncorroborated testimony of an accomplice is sufficient to sustain a conviction if the testimony is not otherwise incredible or unsubstantial on its face.’ ” Vaughn, 410 F.3d at 1004 (quoting United States v. Dunn, 494 F.2d 1280, 1281-82 (8th Cir.1974)). “It is the function of the [trier of fact], not an appellate court, to resolve conflicts in testimony or judge the credibility of witnesses.” Hernandez, 569 F.3d at 897 (quoting United States v. Harrison, 671 F.2d 1159, 1162 (8th Cir.1982)). “Such credibility findings are virtually ‘unreviewable on appeal.’ ” Id. (quoting Boyce, 564 F.3d at 916) (internal marks omitted). The district court expressly found Shannon, Dixon, Ferguson and Lee gave credible testimony concerning Edwards’s involvement in the conspiracies to distribute crack cocaine and possess firearms in relation to the drug trafficking. The district court was in the best position to observe the witnesses’ demeanor and assess their credibility, and we will not disturb the district court’s reasoned credibility determinations.
“[V]iewing evidence in the light most favorable to the government, resolving conflicts in the government’s favor, and accepting all reasonable inferences that support the verdict,” Lockett, 601 F.3d at 840, we find the government presented sufficient evidence for a reasonable jury to find Edwards guilty beyond a reasonable doubt of participating in the crack cocaine and firearms conspiracies. See Gray, 869 F.3d at 1028; see also Lopez, 443 F.3d at 1030 (“[A] defendant may be convicted for even a minor role in a conspiracy, so long as the government proves beyond a reasonable doubt that he or she was a member of the conspiracy.”).
2. Evidentiary Issues
Edwards next argues the district court abused its discretion “by admitting evidence of 21 incidents involving RTB members that had nothing to do with Mr. Edwards” and by admitting “Edwards’ prison correspondence, notes and photographs allegedly related to the RTBs that had nothing to do with drugs or firearms.” Edwards maintains the prejudicial effect of this evidence substantially outweighed any probative value. Edwards suggests the government attempted to equate Edwards’s RTB membership with criminality, and “[t]he district court heavily relied on the inflammatory gang evidence” in convicting Edwards of the crack cocaine and firearms conspiracies. Edwards makes general arguments in support of his position, but directs us to only one specific incident and one specific piece of evidence that he believes were erroneously admitted.
“We review a district court’s evidentiary rulings for abuse of discretion.” United States v. Smith, 591 F.3d 974, 979 (8th Cir.2010). “‘We will not reverse a judgment on the basis of erroneous evidentiary rulings absent a showing that those rulings had a substantial influence on the jury’s verdict.’ ” Id. (quoting United States v. Haskell, 468 F.3d 1064, 1074 (8th Cir.2006)). “Under [Fed. R.Evid.] 403, ‘great deference’ is given to a district court’s balancing of the relative value of a piece of evidence and its prejudicial effect.” Jiminez, 487 F.3d at 1145 [815]*815(quoting United States v. Lupino, 301 F.3d 642, 646 (8th Cir.2002)); see Fed.R.Evid. 403 (“Although relevant, evidence may be excluded if its probative value is substantially outweighed by the danger of unfair prejudice, confusion of the issues, or misleading the jury, or by considerations of undue delay, waste of time, or needless presentation of cumulative evidence.”). “Moreover, the discretion accorded lower courts in determining admissibility of evidence is particularly broad in a conspiracy trial.” United States v. Willis, 997 F.2d 407, 414 (8th Cir.1993) (quoting United States v. Kroh, 915 F.2d 326, 331 (8th Cir.1990) (en banc)) (internal marks omitted).
In the district court’s findings of fact and conclusions of law, the court explained its findings were not based on Edwards’s RTB membership; instead, the court made an explicit finding that Edwards was a participant in the RTB members’ agreement or understanding to sell crack cocaine and to possess firearms in connection with the drug trafficking. “In a conspiracy case, ‘each member of a conspiracy may be held criminally liable for any substantive crime committed by a co-conspirator in the course and furtherance of the conspiracy, even though those members did not participate in or agree to the specific criminal act.’ ” United States v. Johnston, 353 F.3d 617, 624 (8th Cir.2003) (quoting United States v. Escobar, 50 F.3d 1414, 1420 (8th Cir.1995)). Such evidence is relevant when it “illustrate^] the extent of the conspiracy’s operation.” Id. We also have a little more confidence on close evidentiary issues when the district court is the trier of fact and will itself sort through the evidence in arriving at a verdict. The district court did not abuse its discretion in admitting evidence relating to activities of Edwards’s co-conspirators.
3. Prosecutorial Misconduct
Edwards claims the government engaged in prosecutorial misconduct by asking leading questions twenty-four times, intimidating Edwards’s supporters in the courtroom, and referring to the stricken testimony of one of Edwards’s witnesses in the government’s written closing argument.
To obtain a reversal based on prosecutorial misconduct to which there was proper objection, a defendant must show that (1) the prosecutor’s remarks or conduct were improper, and (2) the remarks or conduct affected the defendant’s substantial rights so as to deprive him of a fair trial. If the remarks were improper, then we determine whether they deprived the defendant of a fair trial by examining the cumulative effect of the misconduct, the strength of the properly admitted evidence of the defendant’s guilt, and any curative actions taken by the trial judge.
United States v. New, 491 F.3d 369, 377 (8th Cir.2007) (internal citation omitted). “The ultimate question is ‘whether the prosecutor’s comments, if improper, so infected the trial with unfairness as to make the resulting conviction a denial of due process.’ ” Id. (quoting United States v. Mullins, 446 F.3d 750, 757 (8th Cir.2006)).
“[Although Federal Rule of Evidence 611(c) generally discourages the use of leading questions on direct [examination], it is not automatically improper for the prosecutor to ask such questions or for the district court to permit their use.” United States v. Fenner, 600 F.3d 1014, 1022 (8th Cir.2010). Leading questions on direct examination are permitted “to develop the witness’ testimony” and to inquire of a hostile or adverse witness. Fed. R.Evid. 611(c). “[T]he trial judge has wide latitude in permitting leading questions because he or she is in the best [816]*816position to determine the need for them.” Fenner, 600 F.3d at 1022. Edwards alleges the government continued to ask leading questions despite the fact the district court sustained Edwards’s objection to a leading question on at least twenty-four occasions, and the cumulative effect of the leading questions tainted the district court’s verdict and warrants reversal. We disagree. Edwards’s trial lasted nine days, and we cannot say twenty-four instances of leading questions over the course of the trial so affected Edwards’s substantial rights as to deprive him of a fair trial.
Similarly we find no prosecutorial misconduct based on the government’s questioning of Ferguson. During Ferguson’s direct examination, counsel for the government left the podium to point out people sitting in the gallery of the courtroom and asked Ferguson whether he recognized them. The district court asked counsel to return to the front of the courtroom, but allowed the questioning to continue. Counsel for the government asked Ferguson why he thought the people were in the courtroom, and Ferguson responded, “Probably to intimidate me or getting me to change what I’m saying about [Edwards].” The people in the back of the courtroom were Edwards’s brothers, cousin, and nephews. The question as framed was speculative and lacked foundation as to why the people actually were present, but was relevant and admissible to show Ferguson’s state of mind in recognizing the people present. The district court found no misconduct and denied Edwards’s motion to dismiss the case based on deprivation of Edwards’s Sixth Amendment rights. We agree with the district court. Assuming, without deciding, the government’s conduct in pointing out specific members of the gallery was improper, we would nevertheless conclude this conduct did not deprive Edwards of a fair trial.
Finally, Edwards claims prosecutorial misconduct based on the government’s reference in its written closing argument to the stricken testimony of one of Edwards’s witnesses, Armel Green. Four days before the government submitted its written closing argument, the district court entered an order striking Green’s testimony in its entirety for lack of credibility and probative value. The government’s written closing argument addressed Green’s testimony, urging the district court, “Greene’s testimony should not be stricken from the record, but it should be disregarded in its entirety, because it is false.” We find no misconduct. The district court was aware of its decision to strike Green’s testimony, saying “Green’s testimony [is] so lacking in credibility ... [it] would have had no bearing on this Court’s decision.” The government’s reference to the testimony was harmless.
4. Judicial Bias
Edwards claims he did not receive a fair trial because the district court was biased against him. According to Edwards,
[t]he district court judge established that he was personally biased against Mr. Edwards through the combination of [the court’s] criticism of Edwards’ trivial act of greeting court staff by her first name, anger expressed towards counsel during the proceedings, and concluding the trial with a personal anecdote of how he got revenge on people who were rude.
Edwards failed to raise the issue of judicial bias before the district court. We thus review this claim for plain error. See United States v. Sypolt, 346 F.3d 838, 839 (8th Cir.2003). “In order to prevail, [a defendant] must show that the district court’s failure to recuse was clearly im[817]*817proper under the law, affected his substantial rights, and seriously affected the fairness, integrity, or public reputation of judicial proceedings.” Id. at 839 (quoting United States v. Olano, 507 U.S. 725, 736, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993)) (internal marks omitted).
The Supreme Court has specifically held that “expressions of impatience, dissatisfaction, annoyance, and even anger” are not sufficient to trigger [28 U.S.C. § 455(a)]. And where a judge’s opinions are based on “facts introduced or events occurring in the course of the current proceedings,” those opinions warrant recusal ... only if they “display a deep-seated favoritism or antagonism that would make fair judgment impossible.”
Id. (quoting Liteky v. United States, 510 U.S. 540, 555-56, 114 S.Ct. 1147, 127 L.Ed.2d 474 (1994)) (internal citation omitted).
Edwards admits “the district court’s expressions of bias in the instant case were limited and subtle.” This admission undermines any claim of judicial bias. Having reviewed the record, we conclude the judicial conduct of which Edwards complains simply did not rise to the level of judicial bias and certainly did not affect the fairness of Edwards’s trial.
5. Bill of Particulars
Edwards claims the district court erred in denying his motion for a bill of particulars. Edwards maintains, because the indictment was twenty-seven pages long, involved twelve defendants and two seventeen year conspiracies, and provided no information on specific acts by Edwards, he was entitled to a bill of particulars. The magistrate judge3 denied the motion, and the district court affirmed.
“We review a district court’s denial of a motion for a bill of particulars for an abuse of discretion.” United States v. Livingstone, 576 F.3d 881, 883 (8th Cir.2009). “A bill of particulars serves to in form the defendant of the nature of the charge against him with sufficient precision to enable him to prepare for trial, to avoid or minimize the danger of surprise at trial.... ” United States v. Hernandez, 299 F.3d 984, 989-90 (8th Cir.2002).
An indictment will ordinarily be held sufficient unless it is so defective that it cannot be said, by any reasonable construction, to charge the offense for which the defendant was convicted. To establish reversible error from the denial of a motion for a bill of particulars, a defendant must show that he was actually surprised at trial and suffered prejudice from the denial.
United States v. Fleming, 8 F.3d 1264, 1265 (8th Cir.1993) (internal citation omitted). Having reviewed the indictment and the magistrate judge’s order, we conclude the indictment was sufficient to enable Edwards to prepare for trial and the magistrate judge did not abuse her discretion in denying Edwards’s motion. Edwards also fails to show any actual surprise at trial or any prejudice.
6. Motion to Dismiss the Indictment
Edwards claims the district court erred in denying his motion to dismiss the indictment because the indictment was obtained solely on general hearsay testimony of a police officer. We disagree.
“[T]he Constitution does not prohibit the use of hearsay testimony in grand jury proceedings, and even an in[818]*818dictment based exclusively on hearsay may be valid.” United States v. Hintzman, 806 F.2d 840, 843 (8th Cir.1986) (internal citations omitted). “ ‘The remedy of dismissal for an indictment due to grand jury abuse is appropriate only upon a showing of actual prejudice to the accused.’ ” United States v. Wilson, 565 F.3d 1059, 1070 (8th Cir.2009) (quoting United States v. Kouba, 822 F.2d 768, 774 (8th Cir.1987)). “A petit jury’s subsequent guilty verdict not only means that there was probable cause to believe that the defendant was guilty as charged, but that he was in fact guilty as charged beyond a reasonable doubt.” Id. (quoting Kouba, 822 F.2d at 774) (internal marks omitted). Assuming for argument’s sake there was an error at the grand jury level in obtaining the indictment, any error was harmless because the district court found there was sufficient evidence to convict Edwards beyond a reasonable doubt.
7. Witness Statements
Next, Edwards claims the district court abused its discretion in declining to order the prosecution to disclose the statements of witnesses who were interviewed by the prosecution and did not initially identify Edwards as being involved in the conspiracy. Before trial, Edwards claimed he was entitled to disclosure of these statements pursuant to Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), because the witnesses’ failure to identify Edwards was exculpatory evidence. After an in camera inspection of the witness statements, the district court ordered disclosure of a portion of one of the witness statements and found the others did not contain exculpatory evidence. Edwards suggests this ruling was in error and speculates he might have been entitled to further disclosures.
“Mere speculation that a government file may contain Brady material is not sufficient to require a remand for in camera inspection, much less reversal for a new trial. A due process standard which is satisfied by mere speculation would convert Brady into a discovery device and impose an undue burden upon the district court.” United States v. Pou, 953 F.2d 363, 366-67 (8th Cir.1992) (quoting United States v. Navarro, 737 F.2d 625, 631 (7th Cir.1984)). Here the district court discussed the matter with the parties, reviewed the statements, and ordered disclosure of a portion of one statement. Edwards’s argument is mere speculation, and, therefore, he fails to meet his burden to prove “there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.” United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985).
8. Sentence
Finally, Edwards claims the district court imposed an unreasonable sentence. Edwards acknowledges he received a below Guidelines sentence, but insists the district court erred in (1) failing to find Edwards was entitled to a role reduction based on his minimal/minor participation pursuant to U.S.S.G. § 3B1.2, (2) declining to vary downward based on the sentencing disparity between crack and powder cocaine offenses, (3) failing to consider the sentencing disparity among Edwards’s co-defendants under 18 U.S.C. § 3553(a)(6), and (4) failing to give Edwards sufficient credit for time served.
We review the district court’s interpretation of the Guidelines de novo, and we review for clear error the district court’s application of the Guidelines to the facts. See United States v. Rutherford, 599 F.3d 817, 820 (8th Cir.2010). “We review the district court’s refusal to grant a minor role adjustment for clear error.” [819]*819United States v. Price, 542 F.3d 617, 622 (8th Cir.2008). The district court found “Edwards’ role wasn’t substantially less than most of the people” in the conspiracy. Based on the record in the case, we cannot say the district court clearly erred in denying Edwards a minor role reduction.
Like Bowie, Edwards claims the district court abused its discretion in refusing to consider the sentencing disparity between powder and crack cocaine offenses. For the reasons we stated in our discussion of Bowie’s challenge to his sentence, we conclude the district court did not abuse its discretion in declining to vary downward based on Kimbrough.
Edwards next protests the district court failed to give appropriate consideration to § 3553(a)(6) and created an unwarranted sentencing disparity between Edwards and other members of the conspiracy. Edwards acknowledges his co-defendants were given reductions for cooperation, but he urges the disparity was not justified because the other defendants were more culpable and dangerous. However, Edwards was not similarly situated to his co-defendants who pled guilty and cooperated with the government. See United States v. Cain, 487 F.3d 1108, 1115 (8th Cir.2007) (finding a defendant was not similarly situated to his co-defendants because they pled guilty and cooperated with the government). Our review of the record reveals no abuse of discretion in the district court’s consideration of the § 3558(a) sentencing factors.
Finally, Edwards claims the district court failed to credit the time he had served. The district court reviewed Edwards’s request and amended the judgment twice, ultimately reducing Edwards’s sentence of 216 months to 206 months imprisonment. Edwards objects to the fact the district court did not give him further credit for time served on supervised release violations, but he provides no authority for such a result and no evidence concerning the days for which he should have been credited. Edwards has not shown the district court abused its considerable discretion in fashioning an appropriate sentence.
III. CONCLUSION
We affirm the judgments of the district court and Bowie’s and Edwards’s sentences.