
673 F.3d 854 (2012)
UNITED STATES of America, Appellee,
v.
Yusef Tareek STROUD, Appellant.
Nos. 10-3621, 11-2119.
United States Court of Appeals, Eighth Circuit.
Submitted: December 14, 2011.
Filed: March 14, 2012.
*857 James Schottel, Jr., CJA, argued, St. Louis, MO, for appellant.
Michael A. Bert, AUSA, argued, St. Louis, MO, for appellee.
Before WOLLMAN, MELLOY, and COLLOTON, Circuit Judges.
WOLLMAN, Circuit Judge.
Yusuf Tareek Stroud[1] was convicted of being a felon in possession of a firearm, in violation of 18 U.S.C. § 922(g)(1). The district court[2] sentenced Stroud to 120 months' imprisonment. Stroud appeals his conviction and sentence. He also appeals from the denial of his motion for new trial based upon his claim of newly discovered evidence. We affirm.

I.
On the evening of May 14, 2005, St. Louis Police Officers Michael Scego and Daniel Earley heard shots fired and saw Stroud running while clutching his waistband. From their patrol car, Scego and Earley told Stroud to stop, but he continued to run. The officers initially pursued Stroud by car, but then Earley exited the car and pursued Stroud on foot while Scego followed in the car. While running, Stroud pulled off one of two t-shirts he was wearing. According to Earley, Stroud *858 appeared to wrap the shirt around an object.
Stroud ran between two houses, and Earley continued his pursuit. By this time, Scego had begun following Stroud and Earley on foot. Stroud attempted to climb over a privacy fence, but Earley grabbed his shoulder and pulled him back. Earley then observed the end of a revolver protruding from the rolled up t-shirt in Stroud's hands. Earley struck Stroud twice on the head with his pistol, and Stroud fell, hitting his head against a stone foundation. Stroud continued to struggle, stood up, and threw the t-shirt and gun over the fence. Once Stroud was handcuffed and under arrest, Scego stayed with him while Earley retrieved the items thrown over the fence. Stroud was taken to the hospital and released when medical personnel determined that he was fit for confinement.
Aaron Davis's body was found a few blocks away from the site of Stroud's arrest. The Medical Examiner's Office determined that Davis died of gunshot wounds to the head and upper body. One of the bullets removed from Davis's body was fired from the .357 magnum revolver seized during Stroud's arrest, but analysis of the other bullets was inconclusive.
Stroud was advised of his Miranda rights at the police station. He spoke to police, first stating that he wanted a deal to serve his time in a federal correctional facility. Stroud also nodded his head affirmatively when asked if he had possessed the gun and if he had shot Davis. Stroud later admitted that he had shot Davis to satisfy a heroin debt.
Stroud was charged in state court with murder and armed criminal action. While awaiting trial, he filed a pro se lawsuit under 42 U.S.C. § 1983, alleging that his civil rights had been violated and naming several police officers and detectives, including Scego and Earley, as defendants. On February 14, 2008, Stroud was acquitted of both state charges. Shortly thereafter, the United States Attorney's Office (USAO) opened this case. In July 2008, Stroud's counsel entered an appearance in the civil suit and filed an amended complaint. On September 23, 2008, the Department of Justice (DOJ) received the USAO request for a "Petite waiver."[3] The request was granted on November 6, 2008, and the indictment was filed on December 11, 2008.
Stroud moved to dismiss the indictment, arguing that the federal charges constituted a vindictive prosecution in retaliation for his § 1983 action. His motion was denied. During the trial, Stroud objected to the court's limitations on his cross-examination of Earley, whom he sought to cross-examine on what, in Stroud's view, were inconsistent statements. Specifically, Stroud wanted to question Earley on whether he had struck Stroud "twice" or "several times" with his pistol. The district court ruled that this was a collateral matter, not material impeachment, and ended the line of questioning. The district court also limited cross-examination when Stroud's counsel asked Earley if he had personally measured the distance between the privacy fence and the location where the gun was found, and Earley replied that he had not. Stroud wanted to impeach Earley with his prior sworn statement that "you could see the gun go about 27 feet," but the district court ruled that the prior statement was not inconsistent with the question asked.
*859 Stroud also objected to the admission into evidence of his prior conviction for unlawful possession of a machine gun. The district court ruled that the conviction could be admitted for the limited purposes of proving knowledge, motive, opportunity, and intent under Rule 404(b) of the Federal Rules of Evidence, and gave a limiting instruction to the jury to that effect. At the close of the prosecution's case, Stroud moved for a motion of acquittal, which was denied. The jury found Stroud guilty of being a felon in possession of a firearm.
At sentencing, the district court found by a preponderance of the evidence that Stroud had murdered Davis, applied the enhancement set forth in § 2K2.1(c) of the United States Sentencing Guidelines (Guidelines), and sentenced Stroud to 120 months' imprisonment.
After he filed his appeal from his sentence and conviction, Stroud filed a second appeal, this one from the district court's denial of his motion for new trial. At Stroud's trial, Earley and Scego testified that they had prepared a "joint memorandum" after Stroud's arrest. The prosecution was unable to produce the memorandum. Several witnesses testified that such internal memoranda were routinely destroyed once a formal police report was completed. A copy of the joint memorandum was later mailed to Stroud's counsel as part of discovery in his civil suit. Stroud argues that the joint memorandum constitutes newly discovered evidence and warrants a new trial. The two appeals have been consolidated.

II.

A. Denial of Stroud's Motion to Dismiss the Indictment
Stroud contends that the indictment against him should have been dismissed because he was prosecuted in retaliation for filing a § 1983 action that claimed his constitutional rights were violated. We review the district court's denial of a motion to dismiss an indictment on a claim of vindictive prosecution for abuse of discretion. United States v. Scott, 610 F.3d 1009, 1017 (8th Cir.2010) (citing United States v. Hirsch, 360 F.3d 860, 863 (8th Cir.2004)).
"Although the government may take action to punish a defendant for committing a crime, punishing a defendant for exercising his valid legal rights is impermissible prosecutorial vindictiveness." United States v. Campbell, 410 F.3d 456, 461 (8th Cir.2005) (citing United States v. Goodwin, 457 U.S. 368, 372, 102 S.Ct. 2485, 73 L.Ed.2d 74 (1982)). It is the defendant's burden to show that the prosecution was vindictive, and "[t]he defendant's burden is a heavy one" in light of the discretion prosecutors are given in performing their duties. United States v. Leathers, 354 F.3d 955, 961 (8th Cir.2004) (citing United States v. Kelley, 152 F.3d 881, 885-86 (8th Cir.1998)). Prosecutorial vindictiveness may be proven through objective evidence or through a presumption of vindictiveness "where there exists a reasonable likelihood of vindictiveness, which may arise when prosecutors increase the number or severity of charges." Campbell, 410 F.3d at 461 (citations omitted).
Stroud has failed to provide any objective evidence of vindictiveness and has failed to submit any evidence that would raise a presumption of vindictiveness. In support of his claim, Stroud offers a timeline showing that the USAO, despite having an open case file, did not request a Petite waiver from the DOJ until two months after Stroud's counsel became involved in the § 1983 case. Stroud also points to the magistrate judge's comment during the hearing on his motion to dismiss the indictment that the timing "is *860 enough to maybe raise some eyebrows here." Hr'g Tr. of Aug. 20, 2009, at 7. That comment aside, we agree with the magistrate judge and the district court that the time sequence in this case is insufficient to raise a presumption of vindictiveness. See, e.g., United States v. Johnson, 91 F.3d 695 (5th Cir.1996). Additionally, there was no evidence that the federal prosecutors were even aware of the pending civil lawsuit at the time that the federal charges were brought. See Johnson, 91 F.3d at 699. The district court thus did not abuse its discretion in denying Stroud's motion to dismiss the indictment. Moreover, it was within the district court's discretion to deny Stroud's request for discovery on his claim of vindictive prosecution, as the magistrate judge had already held a hearing on the motion to dismiss and concluded that Stroud had not made a showing sufficient to warrant discovery. Hr'g Tr. of Aug. 20, 2009, at 10.
Stroud's claim that the denial of his motion to dismiss the indictment resulted in a double jeopardy violation is without merit. Prosecution of a federal offense after the prosecution of a state offense arising out of the same acts does not violate the Double Jeopardy Clause. See United States v. Basile, 109 F.3d 1304, 1306-07 (8th Cir.1997) (citing Abbate v. United States, 359 U.S. 187, 194, 79 S.Ct. 666, 3 L.Ed.2d 729 (1959)).

B. Limitations on Cross-Examination
Stroud argues that the district court abused its discretion in limiting his cross-examination of Earley. We will not reverse a district court's decision to limit cross-examination "unless there has been a clear abuse of discretion and a showing of prejudice to the defendant." United States v. Oaks, 606 F.3d 530, 540 (8th Cir.2010) (citing United States v. Brown, 110 F.3d 605, 611 (8th Cir.1997)). The Sixth Amendment guarantees the defendant "an opportunity for effective cross-examination," but the court "retain[s] wide latitude insofar as the Confrontation Clause is concerned to impose reasonable limits on such cross-examination. . . ." Id. at 539-40 (citations omitted). To show a Confrontation Clause violation, a defendant must show that "a reasonable jury might have received a significantly different impression of a witness's credibility had counsel been allowed to pursue the proposed line of cross-examination." Id. at 540 (citing Harrington v. Iowa, 109 F.3d 1275, 1277 (8th Cir.1997)). The district court acted within its discretion in limiting cross-examination. Neither of Stroud's attempts at impeachment would have significantly changed a reasonable jury's impression of Earley's testimony, which, we note, was supported by the testimony of other officers.

C. Admission of Prior Conviction for Possession of a Machine Gun
Stroud argues that the district court abused its discretion in admitting into evidence his prior conviction for possession of a machine gun. "We review evidentiary rulings of the district court for abuse of discretion, and will reverse a district court's decision to admit evidence under 404(b) only if such evidence `had no bearing on the case and was introduced solely to prove the defendant's propensity to commit criminal acts.'" United States v. Cowling, 648 F.3d 690, 699 (8th Cir. 2011) (citation omitted). Evidence of prior convictions is not permissible to prove that a defendant acted in conformity with a propensity to commit acts of that type, but may be admissible for other purposes, such as proving motive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident. Fed.R.Evid. 404(b). The evidence must be *861 "(1) relevant to a material issue; (2) similar in kind and not overly remote in time to the crime charged; (3) supported by sufficient evidence; and (4) higher in probative value than prejudicial effect." United States v. Walker, 470 F.3d 1271, 1274 (8th Cir.2006) (quoting United States v. Strong, 415 F.3d 902, 905 (8th Cir. 2005)).
Stroud argues that his prior conviction is not relevant to a material issue, is not similar in kind and is too remote in time, and is not more probative than prejudicial. We disagree, for the prior conviction for possession of a machine gun is relevant to Stroud's familiarity with and knowledge that he possessed a firearm, which is an element of the offense and therefore material. "Evidence that a defendant possessed a firearm on a previous occasion is relevant to show knowledge and intent. . . ." Walker, 470 F.3d at 1274 (citing Strong, 415 F.3d at 905). The conviction for possession of a machine gun is also sufficiently similar to the current offense and close enough in time to meet our standards of reasonableness. See Walker, 470 F.3d 1271 (upholding admission of an 18 year-old conviction for armed robbery in a felon in possession case); Strong, 415 F.3d at 905-06 (upholding admission of 16 year-old conviction for robbery and being a felon in possession of a firearm). Stroud's previous conviction for possession of a machine gun also involved illegal possession of a firearm and occurred in 1998, less than seven years before the acts at issue in this case. Finally, the admission of Stroud's prior conviction was more probative than prejudicial. "The district court's determination that the probative value of the evidence outweighed any prejudice is afforded substantial deference, and a limiting instruction diminishes the danger of unfair prejudice arising from the admission of the evidence." Walker, 470 F.3d at 1275 (citations omitted). Here, the prior conviction was relevant to an element of the offense, Stroud's knowledge of his possession of the firearm, and the district court instructed the jury regarding the purposes for which the evidence could be considered. Thus, the admission of Stroud's prior conviction for possession of a machine gun was not an abuse of discretion.

D. Denial of Motion for a Judgment of Acquittal
Stroud next alleges that the district court erred in denying his motion for a judgment of acquittal. We review denial of a motion for a judgment of acquittal de novo. United States v. White Bull, 646 F.3d 1082, 1087 (8th Cir.2011). "In reviewing for sufficiency of the evidence, we view the evidence in the light most favorable to the verdict, and we will `overturn a conviction only if no reasonable jury could have concluded that the defendant was guilty beyond a reasonable doubt on each essential element of the charge.'" Id. (quoting United States v. Kenyon, 397 F.3d 1071, 1076 (8th Cir.2005)).
To convict Stroud of being a felon in possession of a firearm, the government was required to prove beyond a reasonable doubt that (1) Stroud had previously been convicted of a felony, (2) he knowingly possessed a firearm, and (3) there was an interstate nexus. United States v. Maxwell, 363 F.3d 815, 818 (8th Cir.2004). Stroud contests only the second element. He claims that Earley and Scego gave conflicting accounts of the events and that their testimony, combined with the lack of fingerprints on the gun, is legally insufficient to support the verdict. Stroud is incorrect. Earley and Scego's testimony, although not identical, was substantially the same. Both testified that they heard shots, saw Stroud running, pursued *862 him, and later saw him throw the firearm. Their accounts differ in the details of exactly when Scego caught up to Earley and Stroud and the degree to which Stroud struggled in the moments before his arrest. Additionally, the jury was presented with the testimony of a third officer, Detective Matt Hanewinkel, who testified that Stroud admitted possessing the firearm. Furthermore, the fingerprint examiner testified that she does not often find fingerprints on firearms. A reasonable jury could conclude that this evidence proved Stroud knowingly possessed the firearm.

E. Alleged Procedural Error and Substantive Reasonableness in Sentencing
A district court commits procedural error if it fails to properly calculate the Guidelines range, treats the Guidelines as mandatory, fails to consider § 3553(a) factors, selects a sentence based on clearly erroneous facts, or fails to adequately explain its chosen sentence. United States v. Feemster, 572 F.3d 455, 461 (8th Cir.2009) (en banc) (citing Gall v. United States, 552 U.S. 38, 51, 128 S.Ct. 586, 169 L.Ed.2d 445 (2007)).
Stroud argues that the district court erred in applying the enhancement set forth in Guidelines § 2K2.1(c), which provides for an enhancement to the most analogous homicide offense level if the felon in possession used the firearm in the commission of another offense and death resulted. Stroud argues that the government did not present sufficient evidence to support the district court's finding that he had murdered Davis. Again, we disagree. At sentencing, Hanewinkel testified that Stroud had admitted killing Davis. Additionally, a firearms expert testified that one of the lead projectiles taken from Davis's body matched the gun Stroud possessed. The evidence was thus sufficient for the district court to determine, by a preponderance of the evidence, that Stroud murdered Davis.
We next turn to Stroud's argument that the district court committed procedural error by not adequately explaining his sentence. Because Stroud did not object to the district court's explanation, we review for plain error. United States v. Hill, 552 F.3d 686, 690 (8th Cir. 2009). Plain error is (1) an error; (2) that is plain; and (3) that affects substantial rights. Id. (citations omitted).
The district court stated that the "primary motivating factors today are respect for the law, protecting the public, treatment for Mr. Stroud plays a role. . . ." Sentencing Tr. at 41. The district court went on to say that 120 months' imprisonment was appropriate, given that the Guidelines recommended a sentence of life imprisonment with the enhancement for murder, but that the statutory maximum was 120 months' imprisonment. Id. We do not require a court "to recite the § 3553(a) factors mechanically," but it must be clear that the district court considered them. United States v. Wood, 587 F.3d 882, 884 (8th Cir.2009). Having articulated the specific factors that informed its sentencing decision and discussed the Guidelines recommendation and statutory maximum sentence, the district court committed no error, plain or otherwise.
To the extent that Stroud challenges the substantive reasonableness and constitutionality of his sentence, we find his arguments to be unpersuasive. Stroud's sentence was within the Guidelines range, and he has failed to rebut the presumption of reasonableness accorded to such sentences. Wood, 587 F.3d at 884 (citing United States v. Toothman, 543 F.3d 967, 970 (8th Cir.2008)). Stroud's final argument challenging his sentence is *863 that the use of acquitted conductthat is, the murder of Davisin sentencing violates his constitutional rights under the Fifth and Sixth Amendment. But it is the settled law of our circuit "that the Constitution does not preclude a district court from considering acquitted conduct in sentencing a criminal defendant." United States v. Papakee, 573 F.3d 569, 576 (8th Cir.2009) (citing United States v. Canania, 532 F.3d 764, 771 (8th Cir.2008)) (considering acquitted conduct does not violate a defendant's Fifth or Sixth Amendment rights).

F. Denial of Stroud's Motion for a New Trial
Lastly, Stroud argues that his conviction should be vacated and that he should be given a new trial on the basis of the joint memorandum that was produced in discovery in his civil action. We review the district court's denial of a motion for a new trial based on newly discovered evidence for "a clear abuse of discretion, a rigorous standard." United States v. Rubashkin, 655 F.3d 849, 857 (8th Cir.2011) (citing United States v. Baker, 479 F.3d 574, 577 (8th Cir.2007)). In order to merit a new trial, (1) the newly discovered evidence must have been unknown or unavailable to the defendant at the time of trial; (2) the defendant must have been duly diligent in attempting to uncover it; (3) the newly discovered evidence must be material; and (4) the newly discovered evidence probably will result in an acquittal upon retrial. Id.
The district court correctly determined that the newly discovered joint memorandum does not warrant a new trial. The joint memorandum was prepared by Earley and Scego after arresting Stroud and was later used to draft the official police report of the incident, written by Detective Ralph Campbell. Stroud contends that the joint memorandum was withheld during his trial and that its absence compromised his ability to cross-examine Earley, Scego, and Campbell. Stroud focuses on facts missing from the official police report, specifically, that Earley struck Stroud with his pistol and that Stroud hit his head on the foundation. But, as the district court pointed out, Earley and Scego testified that Earley struck Stroud with his pistol and that Stroud fell against a limestone foundation while they were trying to arrest him. D. Ct. Order of May 12, 2011, at 4. Stroud was able to cross-examine the witnesses on these points and use these facts in his defense. The joint memorandum did not contain any new material information. Its availability would not have significantly enhanced Stroud's ability to cross-examine the officers, and thus it would not probably result in acquittal on retrial.
Stroud further argues that the denial of his motion for a new trial violates his rights under the Fifth Amendment, the Sixth Amendment, and the Jencks Act. "The Jencks Act requires that the prosecutor disclose any statement of a witness in the possession of the United States which relates to the subject testified to by the witness on direct examination." United States v. Douglas, 964 F.2d 738, 741 (8th Cir.1992); 18 U.S.C. § 3500(b). But "[w]e will not overturn a conviction for noncompliance with the Jencks Act where there is no indication of bad faith on the part of the government, nor an indication of prejudice to the defendant." Id. (citing United States v. Roberts, 848 F.2d 906, 908 (8th Cir.1988)).
Stroud has not shown any indication of bad faith on the part of the government or prejudice to his defense. The testimony at the time of trial was that the memorandum did not exist because such documents were routinely destroyed once *864 a final report had been prepared. This joint memorandum was obviously not destroyed, but there is nothing to suggest that the failure to produce it was anything beyond a bureaucratic mistake. The police testified regarding the facts set forth in the joint memorandum, including the injuries to Stroud during the course of his arrest. Stroud had the opportunity to cross-examine the officers on these facts and to use them in his defense.
Because Stroud was not denied a fair trial and had the ability to confront the officers who testified against him, his arguments under the Fifth and Sixth Amendments also fail. "[U]nless a defendant can show bad faith on the part of the police, failure to preserve potentially useful evidence does not constitute denial of due process of law." United States v. Scoggins, 992 F.2d 164, 167 (8th Cir.1993) (citing Arizona v. Youngblood, 488 U.S. 51, 109 S.Ct. 333, 102 L.Ed.2d 281 (1988)). Stroud has not demonstrated bad faith, and the record reveals that the facts contained in the joint memorandum were known to both sides and aired at trial.

III.
The conviction and sentence are affirmed, as is the order denying the motion for new trial.
NOTES
[1]  Throughout the record and the government's brief the spelling "Yusef" is used. The appellant's brief states that the proper spelling of Mr. Stroud's name is Yusuf.
[2]  The Honorable Rodney W. Sippel, United States District Judge for the Eastern District of Missouri.
[3]  "A `Petite Waiver' is generally described as an authorization by the United States Department of Justice to prosecute a defendant for the same transaction of events that have previously been prosecuted in State Court." Gov't's Br. at 6, n. 1.
