
662 F.3d 958 (2011)
UNITED STATES of America, Plaintiff-Appellee,
v.
Adrian D. HARPER, Defendant-Appellant.
No. 10-3010.
United States Court of Appeals, Seventh Circuit.
Argued October 27, 2011.
Decided December 6, 2011.
*959 Kelly B. Watzka (argued), Assistant U.S. Attorney, Office of the United States Attorney, Milwaukee, WI, for Plaintiff-Appellee.
Christopher D. Donovan (argued), Attorney, Pruhs Law Office, S.C., Milwaukee, WI, for Defendant-Appellant.
Before FLAUM, KANNE, and WOOD, Circuit Judges.
WOOD, Circuit Judge.
Adrian Harper was charged and convicted of being a felon in possession of a firearm in violation of 18 U.S.C. §§ 922(g)(1) and 924(e)(1). During his closing argument, Harper's lawyer told the jury that "trials are about the truth." In its rebuttal, the government picked up on that theme and also asked the jury to "look for the truth." Harper now asserts that it was a mistake to tell the jury that it had to ferret out the truth, because this had the effect of relieving the government *960 of its burden to prove guilt beyond a reasonable doubt. On this record, however, we find no reversible error, and we therefore affirm Harper's conviction.

I
At approximately 1:45 in the morning on September 17, 2008, Milwaukee Police Department Officers Hopgood and Emmons heard five gunshots outside Questions, a popular nightclub. Emmons immediately noticed smoke rising out of the passenger side of a black pickup truck, which quickly sped away. Emmons pursued the truck and called for backup. Several police responded; along with Emmons and Hopgood, they stopped the truck and ordered the driver, Terrence Harper (whom we will call Terrence, to avoid confusion), to get out of the truck. Terrence, who is Harper's cousin, complied and was taken into custody.
The officers then ordered Harper, who was seated on the passenger side, to get out of the truck. As Harper did so, Hopgood heard two shell casings fall to the ground. Once he was out, the police inspected the vehicle and found a number of notable items, including a .357 revolver. The gun's handle faced the passenger side of the vehicle while the muzzle was pointed toward the driver's side, strongly suggesting that the gun had been set down by the passenger. Moreover, the gun was hot and thus probably had been fired recently. Finally, the police recovered several used casings from the passenger side of the vehicle, where Harper had been sitting.
This all led to charges against Harper for being a felon in possession of a firearm. The parties stipulated to Harper's prior felony conviction and to the gun's prior travel in interstate commerce. At the conclusion of the trial, the government stated in its closing argument that there could be "no reasonable doubt that anybody but the defendant possessed that gun." In response, Harper's attorney insisted that "trials are about truth." Given the circumstantial nature of the government's evidence, the lawyer continued, the prosecution had not proved Harper's possession of the gun with the "certainty" required to convict. In rebuttal, the government followed up on that suggestion with the statement that "[a] trial is the search for the truth," not a "search for doubt," and it argued that it had "proven . . . beyond a reasonable doubt what the truth is." At a number of other points, both the government and defense counsel referred to the reasonable doubt standard, and the district court instructed the jury both that the statements and arguments of counsel were not to be taken as evidence and that the government bore the burden of proof beyond a reasonable doubt. Even so, Harper believes that these references to a search for the truth amounted to an erroneous instruction on the reasonable doubt standard, that this constituted structural error, and that he is entitled to a new trial.

II
Because Harper failed to object to the remarks alluding to "the truth" during the trial, our review is only for plain error. United States v. Olano, 507 U.S. 725, 731, 113 S.Ct. 1770, 123 L.Ed.2d 508 (1993); United States v. Stark, 507 F.3d 512, 520 (7th Cir.2007). For Harper to prevail, he must show that the court's failure to do anything about these statements was (1) an error, that is (2) plain, and that (3) affected his substantial rights. Olano, 507 U.S. at 732, 113 S.Ct. 1770.

A
Harper alleges that the attorneys' remarks regarding truth amounted to a de facto impermissible instruction on the reasonable *961 doubt standard. He argues that by telling the jurors to "search for the truth," the attorneys asked the jurors to make a binary choice between true and not true, instead of making it clear that their task was to decide whether the prosecution demonstrated beyond a reasonable doubt that its version was the correct one. He asserts that the "truth" language might have been misunderstood by the jurors as an invitation to convict by a mere preponderance of the evidence.
We do not find any error in the attorneys' closing statements, much less plain error. There was nothing wrong with referring to trials as "searches for truth": As we commented at oral argument, trials are searches for the truth; the burden of proof is just a device to allocate the risk of error between the parties. Indeed, both the Supreme Court and this court have repeatedly noted that criminal jury trials serve an important "truth-seeking" function. E.g., United States v. Mezzanatto, 513 U.S. 196, 204-05, 115 S.Ct. 797, 130 L.Ed.2d 697 (1995); Jones v. Basinger, 635 F.3d 1030, 1040-41 (7th Cir. 2011). The attorneys here did no more than to repeat that uncontroversial proposition.
Nor did the attorneys' remarks restate the government's burden of proof. To the contrary, both attorneys emphasized that the prosecution was required to prove its case beyond a reasonable doubt. For example, the government argued in rebuttal that it had "proven . . . beyond a reasonable doubt what the truth is." In total, counsel for both sides referred to the reasonable doubt standard no less than eleven times during their opening and closing statements.
Most importantly, Harper is wrong to equate arguments of counsel with instructions from the court. It is telling that he offers no criticism of the judge's handling of the reasonable doubt burden. After the attorneys gave their closing arguments, the court issued a proper jury instruction on the reasonable doubt standard. Such instructions from the court carry more weight with jurors than do arguments made by attorneys, Boyde v. California, 494 U.S. 370, 384, 110 S.Ct. 1190, 108 L.Ed.2d 316 (1990), and here, we presume that the court's proper instruction ensured that the jury applied the correct standard.

B
Although we find that the district court committed no error, we proceed through the rest of the plain error analysis for completeness. Even if allowing the attorneys to make closing statements that asked the jury to search for the truth left some space for misunderstanding, any error that arose was not plain. Error is plain when it would be "clear" or "obvious" to the district court. Olano, 507 U.S. at 734, 113 S.Ct. 1770. Here, it was far from evident that there was any impropriety in the attorneys' closing arguments.
As we have already discussed, the Supreme Court and this court have emphasized the important truth-seeking role of trials. E.g., Mezzanatto, 513 U.S. at 204-05, 115 S.Ct. 797; Basinger, 635 F.3d at 1040-41. We ourselves in the past have declined to condemn a prosecutor's statement that a jury's "job is not to search for doubt, but to search for the truth." United States v. Anderson, 303 F.3d 847, 857 (7th Cir.2002). Even if we grant that such statements should be made with care, and that parties would be well advised not to risk confusion with the reasonable doubt standard, the only thing that seems plain is that courts have not recognized any absolute prohibitions against referring to the truth in an argument. Thus, even if it was error to allow the attorneys to ask the jury to search for the truth in the way *962 they did here, any such error was not obvious to the district court.

C
Finally, we are satisfied that Harper's substantial rights were not affected by the attorneys' closing arguments. Harper suggests that Sullivan v. Louisiana, 508 U.S. 275, 279, 113 S.Ct. 2078, 124 L.Ed.2d 182 (1993), which ruled that an erroneous instruction from the court on the reasonable doubt standard is a structural trial error and thus never harmless, should apply to an attorney's misstatements of the government's burden of proof. As we already have indicated, we reject the invitation to extend Sullivan from court instructions to attorney arguments. Jurors understand attorneys' statements to be "matters of argument," while they view instructions from the court as "definitive and binding statements of the law." Boyde, 494 U.S. at 384, 110 S.Ct. 1190. We ourselves would err if we equated the two.
Harper alternately argues that the attorneys' remarks regarding the truth require that he receive a new trial under Darden v. Wainwright, 477 U.S. 168, 181-82, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986). Darden involved a state prisoner's argument that his due process rights were violated by the prosecutor's improper closing arguments. By invoking Darden, Harper is forfeiting any argument that would be cognizable in a direct criminal appeal but not in the special setting of collateral relief from a state-court judgment. In order to show a violation of his due process rights, Harper must establish that the attorneys' closing arguments were improper and prejudicial. Id. Analyzing prejudice under Darden requires the consideration of six factors:
(1) whether the prosecutor misstated the evidence, (2) whether the remarks implicate specific rights of the accused, (3) whether the defense invited the response, (4) the trial court's instructions, (5) the weight of the evidence against the defendant, and (6) the defendant's opportunity to rebut.
Howard v. Gramley, 225 F.3d 784, 793 (7th Cir.2000) (citing Darden, 477 U.S. at 181-82, 106 S.Ct. 2464). As applied in the plain error context, these factors "must establish not only that the [statements] denied [the defendant] a fair trial but also that the outcome of the proceedings would have been different absent the [statements]." United States v. Olson, 450 F.3d 655, 674 (7th Cir.2006).
We will assume for the sake of argument only that the first two factors support Harper. The remaining factors, however, favor the governmenta fact that demonstrates yet again the limited utility at the appellate level of these kinds of multifactor tests, however useful they may be as checklists for the trial judges. Harper invited the misstatement because it was his own lawyer who made the first reference to the truth. Second, by failing to object, Harper bypassed any opportunity to rebut the statements. Most importantly, from our standpoint, the district court provided a proper jury instruction on the reasonable doubt standard and the overwhelming weight of the evidence was against Harper. Gramley, 225 F.3d at 793 ("[T]he most important of the Darden factors is the weight of the evidence against the defendant."). Smoke was billowing from the passenger side of the vehicle, where Harper was seated; Hopgood heard casings fall to the ground when Harper climbed out of the truck; and casings were later recovered from that exact spot. The gun was positioned in a way that indicated that the passenger, Harper, was the last person to hold it. Finally, as icing on the cake, the prosecution presented the testimony *963 of another inmate to whom Harper had allegedly confessed. On this record, Harper cannot "establish . . . that the outcome of the proceedings would have been different absent the remark[s]." Olson, 450 F.3d at 674.

III
Harper also contends that his conviction violated his right to due process, because (he asserts) 18 U.S.C. § 922(e) is unconstitutionally vague. Although he concedes that this argument has been foreclosed by the Supreme Court, see, e.g., Sykes v. United States, ___ U.S. ___, 131 S.Ct. 2267, 2277, 180 L.Ed.2d 60 (2011) (finding that § 922(e) "states an intelligible principle and provides guidance that allows a person to conform his or her conduct to the law"), he nevertheless raises the issue to preserve it for further review. We note, without additional comment, that he has done so from our point of view. We AFFIRM the judgment of the district court.
