OPINION
JANE B. STRANCH, Circuit Judge.
Erik Hentzen was convicted, after a jury trial, of receipt and possession of child pornography in violation of 18 U.S.C. § 2252(a)(2) and (a)(4) and was sentenced to 20 years in prison. He now challenges his conviction, arguing that the prosecution’s evidence was insufficient and that a non-contraband video was improperly admitted into evidence. He also contends that his sentence is procedurally and substantively unreasonable. We agree that the video was improperly admitted, but find the error to be harmless. Because Hentzen’s remaining arguments are without merit, we affirm the judgment and sentence of the district court.
I. BACKGROUND
Hentzen was a 25-year-old student at the University of Kentucky with a strong interest in computers. In his apartment, he had seven'computers and 17 related devices. These devices could store seventeen terabytes—or 17,000 gigabytes—of data. He avidly collected music and video files, including pornography, using various peer-to-peer networks, among other means. One of the peer-to-peer networks that he used was called eDonkey, which he accessed using a software client named eMule.
The Kentucky Attorney General’s Cyber Crimes Unit monitors eDonkey and other peer-to-peer networks to find people who share and distribute child pornography. The Unit uses automated software to search the networks for keywords that are associated with child pornography, documenting the IP addresses of computers that are sharing files with those keywords and the “hash values” of those files. Using the hash value, which is a unique fingerprint for each file, the Unit can identify files that match known child pornography files. With this system, an agent found that a large number of child pornography files were being shared from a particular IP address between September and November 2012. The agent identified the address as belonging to an unsecured internet router in Hentzen’s apartment building and traced the files to a laptop in Hentzen’s apartment as the computer that was sharing the files. The laptop was on the keyboard tray, running while closed.
When the agent found the laptop, he saw that several of the recently downloaded files appeared to be child pornography. The agent seized all of Hentzen’s computing devices and submitted them for forensic examination. The forensic examiners found child pornography files on the laptop, a desktop computer, and two external hard drives. The investigators found 6,536 child pornography videos and 554 child pornography images on the various devices, including those files that had been deleted. (It is not clear whether each of these files was unique.) They also found a digital catalogue for child pornography and three copies of an animated virtual child pornography video depicting a child engaging in sexual activity with an adult man.
At trial, Hentzen stipulated- that child pornography files had been found on his computer and that they had been transported in interstate commerce over the internet. The only contested issue at trial was whether Hentzen knew that the files were child pornography when he downloaded and possessed them.
As evidence that Hentzen knew that he was downloading child pornography, the government presented a document representing his last 30 searches on eMule. The search terms included “a number of commonly found child sexual abuse keyword terms,” and each term had been entered individually. The government also presented evidence that two of the still images had been opened in Internet Explorer (or Windows Explorer) and that a folder containing some of the files had been opened using a view that would show thumbnails of the videos and images. Part of the government’s theory was also that Hentzen was intentionally using his neighbor’s wireless router and storing the laptop that downloaded files in his keyboard tray in order to hide his downloading activity. (The government presented no evidence that Hentzen had not also downloaded files using his own wireless connection.)
During its case in chief, the government introduced into evidence several examples of the files found on Hentzen’s computer. These files included nine child pornography videos, portions of which were played for the jury, as well as the catalogue. The examples included recordings of adult men sexually abusing young girls—in one video, an infant. Another video depicted a girl forced to engage in sexual activity with an animal.
The government also presented the animated video, after filing a notice of intent to use other act evidence. At a pretrial conference, Hentzen objected to the admission of the video but the district court overruled the objection. The court agreed to admit the evidence “for the sole purpose of defining or demonstrating the defendant’s knowledge that ... the materials he had were child pornography as opposed to child erotica.” In its written minute entry, the court ordered the exhibit admitted as “relevant to prove the defendant’s knowledge that the materials he possessed were child pornography.” During the trial, the video was introduced as a “thing[] that would indicate a user’s interest in children” and described as a “grooming video” that would be used “for grooming small children to accept sexual conduct with adults.” The title of the video, “NewüPthlolal—Show This Training Video To Your Daughter To Get Her Ready!!— Hussy,” was also presented to the jury. After the video was shown to the jury, the court gave a limiting instruction that the jury should consider it “only as it relates to the government’s claim on the defendant’s knowledge and intent to receive and possess child pornography.” The court further instructed the jury: “Remember that the defendant is only on trial for receipt and possession of actual child pornography, and not for the other crimes related to child—or other acts, excuse me, related to child erotica.” The limiting instruction was repeated as part of the final jury instructions. The government did not refer to the video during its closing. Hentzen did not make any other objections to the questioning regarding the video, the limiting instruction, or the video’s eventual admission.
Hentzen testified on his own behalf and maintained that he did not know that the files he was downloading were child pornography. He testified that he believed that the files had gotten onto his computer in two ways. First, he ran a side business fixing friends’ computers and would copy all of their media files to his hard drives
when he did so. Second, he testified that he would trawl the internet and other sources for “top ... searches of the day” and developed a text file of all possible pornography keywords. He would then copy each of the words into the eMule search box and download any files that the program' told him he did not have. He maintained that he would generally not look at the names of files—merely the statistics on how big it was and how quickly it could download to his computer. He also testified that he had downloaded at least 100,000 media files to his computer, and had not watched most of the files. Instead, he would immediately open 25 different files at once, to see if any of the files prompted an alert that it was corrupted or contained a virus. He would then move the uncorrupted files to a new folder “called sorted, seen, keep, good, something of that nature.” Occasionally, when the downloading software automatically created a folder for a group of files, he would search for other files with that keyword and place them in the same folder.. He testified that he generally used his own router to download, but that his computer automatically connected to the nearest unsecured router when there was an issue with his own.
Hentzen’s former girlfriend and a friend testified that he allowed them to use his apartment and computers. A forensic expert testified about software that the investigators could have used, but did not use, to determine whether Hentzen had viewed any of the files and how Hentzen was pursuing his searches.
Finally, the government presented rebuttal testimony from the investigating forensic examiner regarding the files that were still downloading when Hentzen’s computer was seized. For some of those files, there was no evidence of any other download started at the same time. The examiner opined that those files had been downloaded individually, but also acknowledged that any files that had completed downloading would not be represented in his list.,
Hentzen moved, pursuant to Fed. R. Crim. P. 29, for a judgment of acquittal at the close of the government’s case in chief and again at the end of the presentation of evidence. The court denied the motion, and the jury convicted Hentzen of both counts.
During the sentencing process, the government and Presentence Investigation Report recommended that Hentzen receive a five-level enhancement for distribution for pecuniary gain, U.S.S.G. § 2G2.2(b)(3)(A), due to his use of a file-sharing program that automatically offered child pornography for other users to download. Hentzen argued that the enhancement should not apply because he had set the upload rate an extremely low level. The court determined that the proper enhancement was the two-level increase for general distribution, U.S.S.G. § 2G2.2(b)(3)(F).
Hentzen moved for a
downward variance, presenting letters attesting to his character and a letter from his treating psychiatrist that stated he displayed obsessive-compulsive tendencies toward digital hoarding.
Hentzen’s resulting offense level was 39. With his Criminal History Category of I, the Guideline range was 262 to 327 months in prison. The court granted a downward variance based on Hentzen’s youth and sentenced him to 20 years (240 months) in prison on each count—the equivalent of the statutory maximum for each—to run concurrently.
Hentzen now appeals (1) the denial of a judgment of acquittal, (2) the admission of the animated video, (3) the application of the distribution enhancement, and (4) the substantive reasonableness of his sentence.
II. Discussion
A. Sufficiency of the Evidence
Hentzen challenges the sufficiency of the evidence supporting his convictions. “We review sufficiency of the evidence challenges de novo to determine “whether, after viewing the evidence in the light most favorable to the prosecution,
any
rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.’ ”
United States v. Mathis,
738 F.3d 719, 735 (6th Cir.2013) (quoting
Jackson v. Virginia,
443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979)). “In making this determination, however, we may not reweigh the evidence, reevaluate the credibility of witnesses, or substitute our judgment for that of the jury.”
United States v. Martinez,
430 F.3d 317, 330 (6th Cir.2005).
Hentzen contends that there was insufficient evidence for a rational jury to find that he knew that the files he received and possessed were child pornography. The crimes of receipt and possession of child pornography “incorporate[ ] a scienter requirement as to the character of the materials involved”: The defendant must have known that the files were child pornography to be guilty.
United States v. Brown,
25 F.3d 307, 310 (6th Cir.1994);
see also United States v. X-Citement Video, Inc.,
513 U.S. 64, 115 S.Ct. 464, 130 L.Ed.2d 372 (1994). “Proof of knowledge ... is rarely established by direct evidence.”
United States v. Scruggs,
549 F.2d 1097, 1104 (6th Cir.1977). Instead, knowledge of the contents of material “may be proven by circumstantial evidence.”
United States v. Kussmaul,
987 F.2d 345, 350 n. 4 (6th Cir.1993).
The government presented significant circumstantial evidence that Hentzen affirmatively sought out child pornography files and viewed them once they were on his computer. He had entered as search terms the names of child pornography stu
dios and the name of a child pornography series. His internet history showed that two still images of child pornography had been opened in the Internet Explorer browser (or its analogue, Windows Explorer). Further evidence from the computer’s “link files” suggested that child pornography files had been opened from his external hard drive. From this evidence, a rational juror could infer that Hentzen knew that he was receiving child pornography—because he was searching for the names of child pornography studios—and knew that he possessed child pornography—because he had viewed it.
Hentzen argues that the evidence is insufficient because he presented an alternative explanation for the circumstantial evidence: that in downloading massive amounts of data, he had assembled search terms carelessly; had opened files without looking at them for the sole purpose of weeding out corrupted files; and, although he sought adult pornography, he had no idea that the files on his computer also included child pornography. Hentzen’s explanations were consistent with the circumstantial evidence; thus, a rational jury could have believed him and decided to acquit. But this jury did not, and we must “not reweigh the evidence, reevaluate the credibility of witnesses, or substitute our judgment for that of the jury.”
Martinez,
430 F.3d at 330. The district court was correct to deny Hentzen’s motions for a judgment of acquittal.
B. Animated Video
We now turn to the admission and use of the animated video at trial. Hent-zen objected to the admission of the video as “other acts” evidence under Fed. R. Evid. 404(b), so we review that issue for abuse of discretion, using the three-part analysis discussed in further detail below.
He also points to several other purported trial errors to which he did not object at trial, including the testimony elicited in the course of introducing the video and the limiting instruction. Because Hentzen did not preserve these issues, we review them for plain error.
See Puckett v. United States,
556 U.S. 129, 134-35, 129 S.Ct. 1423, 173 L.Ed.2d 266 (2009).
Rule 404(b) bars evidence of “a crime, wrong, or other act ... to prove a person’s character in order to show that on a particular occasion the person acted in accordance with the character.” Fed. R. Evid. 404(b)(1). Such evidence is admissible, however, if offered for a permissible purpose. Fed. R. Evid. 404(b)(2). “In deciding whether to admit evidence under Rule 404(b), the district court applies a three-step analysis.”
United States v. Mack,
729 F.3d 594, 601 (6th Cir.2013). The district court must first find, based on sufficient evidence, that the other act actually occurred.
United States v. Jenkins,
345 F.3d 928, 937 (6th Cir.2003). Next, the court determines if the acts could be admitted in support of one of the purposes allowed by Rule 404(b), in other words, “whether the evidence is probative of a material issue other than character.”
Id.
Finally, the court decides whether the probative value of the evidence is substantially outweighed by its prejudicial effect.
Id.
We review a district court’s evidentiary-rulings for abuse of discretion, and, in the case of Rule 404(b) determinations, such review requires a three-part analysis, mirroring the district court’s three-part analysis. Un
ited States v. Clay,
667 F.3d 689, 693 (6th Cir.2012). “First, we review for clear error the factual determination that other acts occurred. Second, we review de novo the legal determination that the acts were admissible for a permissible 404(b) purpose.”
Id.
To answer this question, we independently determine whether the evidence is probative of a material issue other than character. Third, “we review for abuse of discretion the determination that the probative value of the evidence is not substantially outweighed by unfair prejudicial impact.”
Id.; see also United States v. Geisen,
612 F.3d 471, 495 (6th Cir.2010) (“it is an abuse of discretion to make errors of law or clear errors of factual determination in evidentiary rulings”) (internal quotation marks omitted).
Hentzen does not challenge the first step of the analysis. There was “sufficient evidence to support a finding by the jury” that Hentzen was in possession of the animated video.
See Huddleston v. United States,
485 U.S. 681, 685, 108 S.Ct. 1496, 99 L.Ed.2d 771 (1988). The video was found in three locations on Hentzen’s hard drives.
The animated video fails to satisfy the second step of our review because it is not probative of a material issue other than character. Our cases refer to three considerations that address this step, whether performed by the district court or our court: “Evidence of other acts is probative of a material issue other than character if (1) the evidence is offered for an admissible purpose, (2) the purpose for which the evidence is offered is material or ‘in issue,’ and (3) the evidence is probative with regard to the purpose for which it is offered.”
United States v. Haywood,
280 F.3d 715, 720 (6th Cir.2002). The district court determined that the animated video was “relevant to prove the defendant’s knowledge that the materials he possessed were child pornography.” Knowledge is an admissible purpose under Rule 404(b), and, as an element of the crime, it is material.
United States v. Johnson,
27 F.3d 1186, 1192 (6th Cir.1994).
The government fails, however, to show that the animated video is probative of the material issue for which it was offered— whether Hentzen was aware of the contents of the files. The government relies on our earliér ■ unpublished decision in
United States v. Caldwell,
181 F.3d 104 (6th Cir.1999) (Table).
Caldwell,
like this case, was a prosecution for possession of child pornography for which the sole defense was lack of knowledge—that Caldwell was unaware of the presence in his house of the child pornography. In that case, the pornography was in physical form. Caldwell’s wife directed investigators to a small room in their house and described it as containing his “stuff.”
Caldwell,
1999 WL 238655 at *1. The room contained a large quantity of child pornography, child erotica, and adult pornography in boxes. There were also “very well kept stacks” of sexual material on the floor, including a stack on the floor containing erotic collages of children.
Id.
On the wall of the room, there was a teddy bear, a doll, and a sign saying “No Parents Admitted Unless Accompanied By A Child.”
Id.
One box that contained a child pornography magazine also contained “a photocopy of Caldwell’s Social Security card and birth certificate.”
Id.
at *2. Another box contained “a folder obtained by Caldwell from a previous employer.”
Id.
Finally, “Caldwell’s fingerprint appeared on a photograph of a clothed child” that was found in a tackle box “intermingled with pictures of naked children.”
Id.
There, we held that the child erotica— neatly stacked and on display in the room—-was admitted as part of the “setting of the case” and also under Rule 404(b).
Id.
at *7. Specifically, we identified two ways that the child erotica was probative of Caldwell’s knowledge—(1) the child erotica was evidence of a sexual interest in children and (2) the total quantity of child erotica and child pornography made it less likely that Caldwell was unaware of its presence.
Id.
The government now argues that these same inferential links apply in Hentzen’s case.
A core problem with the government’s proposed inferential chains is that there is no independent evidence that Hentzen knew he had the animated video on his computer. As the government notes, the copies of the animated video were “literally intermingled with the child pornography.” Hentzen’s possession of the animated video can only have been evidence of his knowledge of the contents of the child pornography if he knew that he had the animated video. But knowledge of the content of the folders is exactly what the government had to prove. To illustrate the problem with this circular logic, consider its analogue in the
Caldwell
case. If Caldwell had been found with a closed box containing both child erotica and child pornography, it would make no sense for the government to point to the child erotica in the same box as evidence that Caldwell knew of the contents in the box. In fact, in Caldwell’s case, there was significant independent evidence that he had seen the child erotica, including the display of some materials on the wall; the fact that child erotica was in a neatly-stacked open pile that Caldwell had moved into the room about two years prior; and the presence of his work and personal materials intermingled with the erotica and child pornography. In contrast, there is no independent evidence that Hentzen ever viewed the animated video or even saw its (profoundly disturbing) title, aside from the evidence that he knew of the child pornography. Nor does the addition of three copies of the animated video to the several thousand child pornography video files among Hent-zen’s 100,000 videos make it more likely that Hentzen was aware of the contents of his computer. In the context of Hentzen’s nearly unlimited hard drive capacity, three copies of a file in an unopened folder would be virtually unnoticeable.
This analysis does not imply that child erotica or virtual child pornography is never probative of a child pornography defendant’s knowledge. If there is independent evidence that the defendant had seen or knew of the child erotica, the erotica could support an inference of a sexual interest in children. For example, in
United States v. Vosburgh,
602 F.3d 512 (3d Cir.2010), investigators had found traces of child pornography files on the defendant’s computer, along with a sizeable collection of child erotica of which the defendant admitted knowledge. Because the defendant admitted to knowledge of the pictures, “[p]os-session of those pictures suggested that Vosburgh harbored a sexual interest in children,” and the admission of the child erotica over a Rule 403 objection was affirmed.
Id.
at 538. Similarly, child erotica contained in a well-visited or visibly marked part of a defendant’s computer may provide sufficient independent evidence of knowledge of the erotica to support its relevance.
Because the animated video is not probative of any material issue, it was error for the district court to admit it. There is then no need to address at length the third step of the Rule 404(b) analysis because the video’s non-existent probative value is substantially outweighed by the clear prejudicial effect of the video in light of its title
and content—the insinuation that Hentzen was preparing to molest a child.
Hentzen is not entitled to a new trial, however, if the error was harmless. “An error in the admission of evidence does not require granting a criminal defendant a new trial unless the error affects ‘substantial rights.’ ”
United States v. DeSantis,
134 F.3d 760, 769 (6th Cir.1998) (quoting Fed. R. Crim. P. 52(a)). “Where an error is not of constitutional dimension, it is harmless unless it is more probable than not that the error materially affected the verdict.”
United States v. Martin,
897 F.2d 1368, 1372 (6th Cir.1990). Whether improperly admitted 404(b) evidence “substantially swayed” a jury “generally depends on whether the properly admissible evidence of the defendant’s guilt was overwhelming.”
United States v. Bell,
516 F.3d 432, 447 (6th Cir.2008). “When the government presents other convincing or overwhelming evidence, we may deem the admission of 404(b) evidence mere harmless error.”
United States v. Layne,
192 F.3d 556, 573 (6th Cir.1999). The burden is on the government to prove that the error was harmless.
United States v. Olano,
507 U.S. 725, 734-35, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993).
In light of the entire record, the government sufficiently established that the error was harmless. The jury saw the animated video after seeing nine properly admitted videos—videos that showed actual children being abused by adult men in horrifying ways—and a catalogue of child pornography. The government reminded the jury of the videos and catalogue in closing. The government also relied on evidence that Hentzen knew of the child pornography, including the evidence from his browser history and his search terms. As for the animated video, it was never referenced after its introduction into evidence nor was there any further insinuation that Hentzen was preparing or had the inclination to molest a child. The limited use of the animated video illustrates its lack of legitimate evidentiary value, but it also weighs against any conclusion that the jury would have decided the case differently absent the introduction of the animated video. We ultimately conclude that the erroneous admission of the video did not materially affect the jury’s verdict.
Nor do the various unpreserved errors regarding the investigator’s testimony about the video and purported flaws in the limiting instruction warrant reversal. Because Hentzen did not object, we can review the issues only for plain error. Fed. R. Crim. P. 52(b). One of the requirements for an error to be plain is that it affected the defendant’s substantial rights.
United States v. Stewart,
306 F.3d 295, 307 (6th Cir.2002). “[T]he substantial rights prong of the plain error analysis is akin to the harmless error analysis employed in preserved error cases. The difference, however, is that under plain error review the burden is on the defendant to show that the error was prejudicial, i.e., that his substantial rights were affected.”
Id.
at 322 (internal quotation marks and citation omitted). The alleged errors in testimony and limiting instruction prejudiced Hent-zen only incrementally more than admission of the video itself. In light of the full record, Hentzen is unable to prove that the errors were sufficiently prejudicial to merit a new trial.
C. Application of U.S.S.G. § 2G2.2(b)(3) for Distribution
“Post-Booker,
we review a district court’s sentencing determination ‘under a deferential abuse-of-discretion standard’ for reasonableness.”
United States v. Bolds,
511 F.3d 568, 578 (6th Cir.2007) (quoting
Gall v. United States,
552 U.S. 38, 41, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007)).
We “must first ensure that the district court committed no significant procedural error, such as failing to calculate (or improperly calculating) the Guidelines range.”
Gall,
552 U.S. at 51, 128 S.Ct. 586. “If the sentence is procedurally sound, we then consider the substantive reasonableness of the sentence imposed.”
United States v. Presley,
547 F.3d 625, 629 (6th Cir.2008) (internal quotation marks omitted).
District courts determine the factual bases for sentencing factors by a preponderance of the evidence.
United States v. Ross,
703 F.3d 856, 884 (6th Cir.2012). We review the district court’s factual findings for clear error and its legal interpretations of the Guidelines de novo.
United States v. Battaglia,
624 F.3d 348, 351 (6th Cir.2010).
Because Hentzen limited the extent to which files were uploaded from his computer, he argues that the district court erred by applying the two-level increase for distribution, U.S.S.G. § 2G2.2(b)(3)(F). Hentzen emphasizes that he limited his upload speed to an extremely low level and moved files out of his shared folder soon after they finished downloading. He describes these actions as preventing his computer from sharing anything with others on eMule. But that is not the test. The Guidelines manual defines distribution as “any act, including possession with intent to distribute, production, transmission, advertisement, and transportation, related to the transfer of material involving the sexual exploitation of a minor.” U.S.S.G. § 2G2.2, comment, (n. 1). The investigators found Hentzen because his computer made several child-pornography files appear available for upload. This advertisement from his computers to other computers was sufficient for application of the distribution enhancement.
D. Substantive Reasonableness of the Sentence
Finally, Hentzen contends that his below-guidelines sentence is substantively unreasonable. “Sentences are substantively unreasonable where ‘the district court chooses the sentence arbitrarily, grounds the sentence on impermissible factors, or unreasonably weighs a pertinent factor.’ ”
United States v. Lumbard,
706 F.3d 716, 727 (6th Cir.2013) (quoting
United States v. Brooks,
628 F.3d 791, 796 (6th Cir.2011)). “A sentence that falls within a properly calculated guideline range is afforded a rebuttable presumption of reasonableness, and it is incumbent upon the defendant to demonstrate that his sentence is unreasonable.”
United States v. Evers,
669 F.3d 645, 661 (6th Cir.2012) (quoting
United States v. Brogdon,
503 F.3d 555, 559 (6th Cir.2007)). It is even more difficult to demonstrate that a below-guidelines sentence is unreasonably long.
United States v. Curry,
536 F.3d 571, 573-74 (6th Cir.2008).
Hentzen argues that the district court failed to properly weigh several of his mitigating circumstances, including his lack of prior criminal history, his psychiatric issues leading to hoarding digital material, and his many character references from friends and family. Under 18 U.S.C. § 3553(a), the sentencing court must consider, among other factors, “the nature and circumstances of the offense and the history and characteristics of the defen
dant.” The record reflects that the court reviewed all of the materials relating to Hentzen’s character and history, including the psychiatric material. (R. 60, PagelD 904-05, 915) That the court gave some factors less weight than Hentzen deemed appropriate is not grounds for reversal. “The fact that [we] might reasonably have concluded that a different sentence was appropriate is insufficient to justify reversal of the district court.”
Gall,
552 U.S. at 51, 128 S.Ct. 586.
Hentzen also points to recent statements by the United States Sentencing Commission and other district courts calling into question the validity of the child-pornography guidelines as a measure of the culpability of defendants. District courts are permitted to exercise their discretion and vary from § 2G2.2 “on reasonable policy grounds as long as the basis for doing so is adequately explained.”
United States v. Ziska,
602 Fed.Appx. 284, 290 (6th Cir.2015). But “the fact that a district court
may
disagree with a Guideline for policy reasons and
may
reject the Guidelines range because of that disagreement does not mean that the court
must
disagree with that Guideline or that it
must
reject the Guidelines range if it disagrees.”
United States v. Brooks,
628 F.3d 791, 800 (6th Cir.2011) (emphasis in original). The court acted within its discretion in declining to reject the Guidelines range for policy reasons.
III. Conclusión
For the foregoing reasons, we affirm the judgment and sentence of the district court.