CUMMINGS, Circuit Judge.

In December 1977, defendant was indicted for conspiring to counterfeit $20 Federal Reserve Notes in violation of 18 U.S.C. § 371. The second count of the indictment charged him with the substantive offense of counterfeiting more than 4500 $20 Federal Reserve Notes (Check Letter and Face Plate H59, Back Plate 202, Series of 1974, with various serial numbers) in violation of 18 U.S.C. § 471. After six trial days, a jury found defendant guilty on both counts. He received a seven-year sentence for the substantive offense and a consecutive term of five years' probation on the conspiracy count. On appeal, defendant raises three grounds to support a new trial or an evidentiary hearing, but we affirm.

I

Defendant's first contention is that newly discovered evidence shows that one of the Government's key witnesses gave perjured testimony, and that a new trial is therefore necessary. The witness involved was Anthony Donato, who was named as a co-conspirator in the indictment but not as a defendant. Defendant asserts that Donato's testimony was perjured and that the result of his post-trial polygraph examination requires the district court to hold an evidentiary hearing on defendant's motion for a new trial under Rule 33 of the Federal Rules of Criminal Procedure.

At Gabriel's trial, Donato related the details of his, Janak's and Gabriel's counterfeiting operation in back of Gabriel's television shop during the first half of 1976. Gabriel's counsel cross-examined Donato thoroughly about the counterfeiting operation, his prior criminal record, his sentencing agreement with the prosecutor, and his possible motives to testify against the defendant. In addition, the Government had Donato testify to the fact that while he was in the penitentiary, he falsely told a visitor (an undercover agent) that he had $1.8 million in counterfeit money buried in the Chicagoland area.

Before Gabriel's trial, Donato admitted to Secret Service agents that he had invented the burial story because he was lonely in prison, his family had deserted him, and the undercover agent was his only prison visitor. The Secret Service investigated Donato's burial story and all leads proved false. As a final effort to check on Donato's burial story, the Secret Service conducted the polygraph examination at issue here on April 18, 1978. As defendant's and the Government's appendices show, the polygraph examination focused on the burial story and did not concern the Worth, Illinois, counterfeiting operation involved in Gabriel's trial. Since the polygraph examination showed deceptive responses to certain questions about Donato's burial of counterfeit money, he was confronted by the Government with the examination results in May 1978 but persisted in his denial of the burial of counterfeit money. At Gabriel's trial, the defense attorney had cross-examined Donato on his conflicting stories and emphasized to the jury that these contradictory stories demonstrated that Donato was unworthy of belief.

The defense's theory on appeal is that the polygraph result, suggesting that Donato may have been lying when he recanted his story about buried counterfeit bills, is new evidence justifying an evidentiary hearing on whether a new trial is necessary. The polygraph examination took place on April 18, five days after the jury returned a guilty verdict against defendant. A copy of the polygraph results was not furnished to the United States Attorney until the first week of June 1978, several weeks after defendant was sentenced. On July 12, 1978, the United States Attorney sent the trial judge and defendant's trial counsel copies of the polygraph examination, stating in part as follows:

"In May 1978, Donato was confronted with the fact that he apparently showed what an examiner concluded to be deceptive reactions during the polygraph examination. Donato again emphatically denied possessing $1.8 million in counterfeit currency and advised that he had fabricated this story while at the Federal Correctional Institution at Safford, Arizona in order to ingratiate himself with the other inmates at the institution and to ease his loneliness while incarcerated. Donato could not explain why he showed such reactions to the polygraph examination and continually emphasized that he did tell the truth in advising the investigating agents that the story was in fact a fabrication. The Secret Service remains unaware of any evidence that corroborates Donato's prison `tale' that counterfeit money was buried.

"While we recognize a broad duty under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963) to disclose information of this nature, it is the government's position that this polygraph examination has no bearing on the conviction and disposition of John Gabriel. First, the focus of the polygraph examination was the possible burial of counterfeit money while the issue at trial involved the printing of counterfeit money at defendant Gabriel's television shop in Worth, Illinois. Thus, the polygraph subject matter is collateral to the issue at trial. Moreover, the direct examination and cross examination of Donato at trial repeatedly brought out the inconsistent statements that Donato had made about the burial of $1.8 million in counterfeit currency.

"Second, the jury obviously believed the corroborated testimony of Donato at trial relative to the counterfeiting operation at Worth, Illinois. Defendant Gabriel testified at trial, and the jury chose to disregard his testimony completely. As noted above Donato remains insistent that his Arizona burial story was false.

"Third, although polygraph examinations are arguably useful investigative tools, federal courts have consistently held evidence of such examinations inadmissible at trial. Accordingly, it would not have been appropriate for the defense to even inquire about a polygraph examination.

"The collective judgment of twelve jurors remains the ultimate arbiter of credibility in our criminal justice system. Accordingly, it is our position that the post-trial polygraph examination of Anthony Donato is immaterial to the judgment and sentence of John Gabriel." (Government's Group Appendix B, pp. 1-2.)

The foregoing communication prompted defendant's new counsel to appear before the district court on July 19, asking leave to file "Post-trial motions based upon evidence supplied by the government, post-trial," but the trial court declined to grant the motion. Relying principally upon Larrison v. United States, 24 F.2d 82 (7th Cir. 1928), defendant claims the district court should have held a hearing on the new trial motion. In Larrison, Judge Evans stated that a new trial should be granted when

"(a) The court is reasonably well satisfied that the testimony given by a material witness is false.

"(b) That without it the jury might have reached a different conclusion.

"(c) That the party seeking the new trial was taken by surprise when the false testimony was given and was unable to meet it or did not know of its falsity until after the trial." ( 24 F.2d at 87-88.)

However, the Larrison court affirmed the six convictions instead of remanding for a new trial. We do likewise.

In Larrison, the key witness later stated that his inculpatory testimony was a complete fabrication. Here the post-trial polygraph examination of Donato was on a collateral matter, so that Judge Bua could properly conclude it was irrelevant to the question whether Gabriel had engaged in the counterfeiting operation in Worth, Illinois. We agree that it was irrelevant to Gabriel's alleged offenses and therefore the denial of his post-trial motion for a new trial is sustainable. Since Judge Bua had heard both Donato and Gabriel testify during the latter's trial, his decision was well within his discretion.

None of the Larrison tests on which defendant relies was satisfied. Donato had always stated that he, Janak and Gabriel printed money in the rear of Gabriel's television shop in early 1976, and Gabriel has been unable to demonstrate that Donato committed perjury in this testimony. Moreover, consistently with his polygraph answers, Donato testified at Gabriel's trial that his fall 1977 burial story was a lie. Even if the polygraph examiner was correct in concluding that Donato "showed deceptive reactions" to two questions about the alleged burial of counterfeit money, that matter was entirely collateral to the trial issue, so that Judge Bua could and did remain satisfied that Donato's relevant testimony was truthful. Additionally, as previously indicated, Gabriel's counsel did attempt to impeach Donato's testimony with these conflicting stories. The evidence of the polygraph results, even if it was admitted, would have been merely cumulative in this attempt to undermine Donato's credibility.

The second Larrison test was whether the jury might have reached a different conclusion without the allegedly false testimony. However, defendant has not shown that Donato's denial of the buried counterfeit money was false. Since he was thoroughly cross-examined about it, the jury was entitled to assess his credibility. It obviously believed Donato on the vital issue of whether Gabriel had printed counterfeit money. Since the issue here is whether the discovery of new evidence tending to impeach the character or credibility of a witness necessitates a new trial, the test is whether the admission of the evidence probably would produce a different result at such new trial. United States v. Barrett, 505 F.2d 1091, 1107 (7th Cir. 1975); United States v. Curran, 465 F.2d 260, 264 (7th Cir. 1972). Even if the district court allowed further impeachment of Donato's testimony by the polygraph results (see note 6 supra) this would probably not produce a different result at a new trial, since he was thoroughly cross-examined regarding both his inconsistent statements about the burial of the money and about motives he might have for testifying against Gabriel. We agree with the Government that it would be pure speculation whether the jury might have reached a different verdict if it knew the results of the polygraph test.

The third Larrison test was not satisfied because defendant was not taken by surprise by the counterfeit burial testimony and was as already indicated able to meet it through cross-examination. Furthermore, its falsity has not really been demonstrated. Finally, Donato's key testimony against Gabriel was amply corroborated by other witnesses and the Government's physical evidence. In view of the overwhelming evidence against defendant, the district court's denial of the motion for a new trial was not erroneous.

II

Defendant next argues that the trial court committed prejudicial error by giving the jury a supplemental Allen charge as modified in United States v. Silvern, 484 F.2d 879, 883 (7th Cir. 1973) ( en banc), after the jury had already received a written modified Allen charge. On April 12, the trial court charged the jury and submitted written instructions for them to consider during their deliberations. One of the instructions was the Allen charge as revised in Silvern.

Several hours after the jurors commenced deliberating, the district court received a note from the jurors stating that they were "hung" 11 to 1 against the defendant. Judge Bua told counsel that two and one-half hours of deliberation were insufficient in that the case had already taken six days to try and that he therefore was prepared to repeat the modified Allen instruction. Accordingly, over defense counsel's objection, the court called the jury back and read them the modified Allen charge. In Silvern, we approved a similar procedure. While defendant relies on United States v. Chaney, 559 F.2d 1094 (7th Cir. 1974), to show that the re-instruction was coercive, there the trial judge gave a supplemental charge that the

"jurors could have understood * * * as meaning that they must reach a verdict to avoid being locked up until 9:30 a. m. In addition, they could have understood the judge to mean that he was too busy to try the case again, so that they must deliberate until reaching a verdict. The supplemental instruction could also be understood as meaning that even though the jurors deliberated until 9:30 a. m., the court might require them to continue deliberating thereafter even though they had been without sleep since the preceding morning. Therefore, this innocently intended instruction cannot pass muster." 559 F.2d at 1098.

No such potentially coercive circumstances were present here, so that it was permissible for the trial judge to repeat the Silvern instruction in this case.

The defendant also attacks certain of the court's instructions to the jury. Over defense counsel's objection at the conference, the trial court charged the jury:

"The word `knowingly' as used in the crime charged means that the act (or omission) was done voluntarily and purposely, and not because of mistake or accident. Knowledge may be proven by defendant's conduct, and by all the facts and circumstances surrounding the case. No person can intentionally avoid knowledge by closing his eyes to facts which should prompt him to investigate."

Defendant objects to the final sentence of his instruction, but we specifically approved it in United States v. Prewitt, 553 F.2d 1082, 1087 (7th Cir. 1977), and adhere to that decision.

While defendant makes three other attacks on the instructions, we find that (1) the trial judge did give a balancing instruction on the government agent's credibility (Tr. 994), (2) defense counsel did not request an instruction instructing the jury how to view the rebuttal testimony of Donato, as required by Rule 30 of the Federal Rules of Criminal Procedure, and (3) the final assailed instruction about the jurors being free to disregard testimony where they did not believe it "except insofar as it may have been corroborated by other credible evidence" was held to be harmless error in United States v. Holland, 537 F.2d 821 (5th Cir. 1976) ( en banc). We agree.

III

Defendant's last argument is that the overall conduct of the case by the Government compels reversal. The first assailed prosecutorial misconduct is the Secret Service's failure to arrest Donato on June 18, 1976, when he gave the government agents a detailed statement of the counterfeiting operation after they searched the Worth, Illinois, premises pursuant to a search warrant. Donato was arrested in October 1976, and Gabriel's present counsel is unable to show why it was an abuse of discretion not to arrest him earlier.

Gabriel's appellate counsel also attacks the Government's decision to indict him and Donato separately. Since Donato had in effect confessed in June 1976 and Gabriel was resisting the Government's investigation, it was perfectly logical for the Government to indict Donato first. Indeed, if they had been indicted jointly, Gabriel's counsel would doubtless have sought a severance.

Gabriel's counsel charges the Government with misconduct in cross-examining defendant as to whether he knew three persons. Gabriel's answers were in the negative. The entire colloquy consumed only 21 lines of the transcript. The persons inquired about had been apprehended for selling counterfeit money to undercover agents. Expert testimony established that the bills involved in this transaction had come from the Worth counterfeiting operation. At a side bar, the prosecutor told the judge what prompted this line of questioning, causing Judge Bua to remark, "You are looking for an open court confession." The prosecutor then said he was not going to pursue the subject any further even though it was a legitimate course of inquiry. Since the jury was not told that the three persons Gabriel denied knowing had been involved in the sale of the counterfeit bills, the inquiry was harmless and it was unnecessary for the Government to follow up defendant's denials with proof to the contrary. Moreover, no prejudice to the defendant has been shown.

Next, Gabriel's counsel challenges parts of the Government's closing and rebuttal arguments to the jury. He objects to the Government informing the jurors that if Donato "lies on the stand, he only faces federal perjury charges" or "opens himself up to perjury." Since this is a true statement and since Gabriel has not shown that Donato lied at this trial, no reversible error was committed in this regard.

In the closing argument of defense counsel, Mr. O'Donnell reminded the jurors that he had asked Donato "whether he was ever given a polygraph test. No. Ask yourselves why. Because they [Government counsel and agents] didn't believe him * * *" (Tr. 954). The response of the prosecutor "that polygraphs are not admissible in a federal trial" (Tr. 977-978) was an invited and generally accurate response (see note 6 supra) and not error.

In concluding, Gabriel's counsel quotes certain remarks of the prosecutors in an effort to show that they were impermissibly pitting the Government against Gabriel. No such objection was made at trial and the remarks are not plain error within Rule 52(b) of the Federal Rules of Criminal Procedure. Also, a presently criticized statement of the prosecutor's "If we come up with any information that is favorable to the defendant, then we must provide it immediately" (Tr. 976) was a response to the defendant's implication that the Government's handwriting experts believed Donato's signature on documents offered by Gabriel to be genuine. It is an accurate paraphrase of Brady v. State of Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215, and not to be condemned.

Judgment affirmed.