Thomas Clyde Bowling, Jr., a Kentucky death row inmate represented by counsel, applied for leave to file a second or successive petition for a writ of habeas corpus pursuant to 28 U.S.C. § 2244. He asserts that he is mentally retarded and therefore ineligible for the death penalty under Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002). Bowling also appeals from a federal district court order denying his motion for relief from judgment pursuant to Fed.R.Civ.P. 60(b). He seeks a certificate of appealability, arguing that his ineffective-assistance-of-counsel claim and his Brady claim should be reopened. We construe his request for a certificate of appealability as an application for leave to file a second or successive petition for a writ of habeas corpus. For the following reasons, we deny both of Bowling’s applications to file a second or successive habeas petition.
I.
In December 1990, a Kentucky state jury tried and convicted Bowling of two counts of murder in the deaths of James and Tina Early. The trial court sentenced him to death. The Supreme Court of Kentucky affirmed the convictions and sentence on direct appeal. Bowling v. Commonwealth, 873 S.W.2d 175 (Ky.1993). In October 1996, the trial court denied Bowling’s petition for post-conviction relief under Ky. R.Crim. P. 11.42. The Supreme Court of Kentucky affirmed the trial court’s decision on appeal. Bowling v. Commonwealth, 981 S.W.2d 545 (Ky.1998).
In August 1999, Bowling filed a petition for a writ of habeas corpus under 28 U.S.C. § 2254 in federal district court. Without ordering an evidentiary hearing, the district court denied the petition, and this court affirmed the district court’s opinion. Bowling v. Parker, 138 F.Supp.2d 821 (E.D.Ky.2001), aff'd, 344 F.3d 487 (6th Cir.2003), cert. denied, — U.S. -, 125 S.Ct. 281, 160 L.Ed.2d 68 (2004).
Bowling subsequently filed an action in Fayette Circuit Court against Warden Glenn Haeberline, claiming that he is exempt from the death penalty because he is mentally retarded. Bowling v. Commonwealth, 163 S.W.3d 361, 364 (Ky.2005). The circuit court summarily dismissed his petition, concluding that Bowling could not collaterally attack his death sentence through a civil action and that he had not timely asserted his mental retardation claim. Id. at 365. Bowling appealed to the Kentucky Supreme Court. The Kentucky Supreme Court held that Bowling procedurally defaulted his claim that he is mentally retarded because he could have asserted such a claim at trial given that Kentucky had in place at that time a statute prohibiting the execution of the mentally retarded. Id. at 371-72. It further determined that Bowling could not make a prima facie showing that he is mentally *436retarded because his I.Q. scores were higher than what Kentucky law considers to be “significantly subaverage intellectual functioning.” Id. at 384.
While the Kentucky state court action was ongoing, Bowling filed an application for leave to file a second or successive petition for a writ of habeas corpus with this court. In his application, he asserts that he is actually innocent of the death penalty because he is mentally retarded. He also filed a Rule 60(b) motion to reopen his first habeas corpus proceeding in the United States District Court for the Eastern District of Kentucky. The district court denied the motion, and Bowling filed a request for a certificate of appealability with this court.
II.
An application for permission from this court to file a second or successive habeas petition must not involve a claim that has been raised in a previous habeas petition. 28 U.S.C. § 2244(b)(1). A new claim will not be allowed to proceed unless:
(A) the applicant shows that the claim relies on a new rule of constitutional law, made retroactive to cases on collateral review by the Supreme Court, that was previously unavailable; or
(B)(i) the factual predicate for the claim could not have been discovered previously through the exercise of due diligence; and
(B)(ii) the facts underlying the claim, if proven and viewed in light of the evidence as a whole, would be sufficient to establish by clear and convincing evidence that, but for constitutional error, no reasonable factfinder would have found the applicant guilty of the underlying offense.
Id. § 2244(b)(2). In order for this court to grant permission to file a second or successive habeas petition, the applicant must make a prima facie showing that his application satisfies the statutory requirements. Id. § 2244(b)(3)(C). A prima facie showing requires the presentation of “sufficient allegations of fact together with some documentation that would ‘warrant a fuller exploration by the district court.’ ” In re Lott, 366 F.3d 431, 433 (6th Cir.2004) (quoting Bennett v. United States, 119 F.3d 468, 469 (7th Cir.1997)).
Bowling’s claim that he cannot receive the death penalty because he is mentally retarded rests upon the new rule established in Atkins, in which the Supreme Court held that the execution of a mentally retarded offender violates the Eighth Amendment. 536 U.S. at 321, 122 S.Ct. 2242. This rule has been made retroactive to cases on collateral review. See Hill v. Anderson, 300 F.3d 679, 681 (6th Cir.2002).
In order for this court to grant Bowling a second or successive habeas petition, Bowling must present “sufficient allegations of fact together with some documentation” of his claim that he is mentally retarded. See Lott, 366 F.3d at 433; In re Holladay, 331 F.3d 1169, 1174 (11th Cir.2003) (establishing that the motion should be granted allowing petitioner to file a successive habeas petition, “if petitioner’s proofs, when measured against the entire record in this case, establish a reasonable likelihood that he is in fact mentally retarded”). Thus, the key substantive question before this court is whether Bowling was mentally retarded at the time he committed the murders of James and Tina Early.
Atkins did not set forth a definitive rule or procedure for the courts to follow in determining when an offender is mentally retarded such that his or her execution would violate the Eighth Amendment. Instead, Atkins reserved for the states “the task of developing appropriate ways to *437enforce the constitutional restriction” upon the execution of sentences. 536 U.S. at 317, 122 S.Ct. 2242.
Atkins specifically observes that “[n]ot all people who claim to be mentally retarded will be so impaired as to fall within the range of mentally retarded offenders about whom there is a national consensus” against execution. Id. Those who are mentally retarded will have “significantly subaverage intellectual functioning, existing concurrently with related limitations in two or more of the following applicable adaptive skill areas: communication, self-care, home living, social skills, community use, self-direction, health and safety, functional academics, leisure, and work.” Id. at 308 n. 3, 122 S.Ct. 2242 (quoting American Association on Mental Retardation, Mental Retardation: Definition, Classification, and Systems of Support 5 (9th ed.1992)). Further, mental retardation will manifest before the person reaches eighteen years of age. Id.
Kentucky law began prohibiting the execution of “seriously mentally retarded” defendants twelve years prior to Atkins. Ky.Rev.Stat. § 532.140. It defines “seriously mentally retarded” as one who has “significant subaverage intellectual functioning existing concurrently with substantial deficits in adaptive behavior and manifested during the developmental period.” Id. § 532.130(2). “Significant subaverage intellectual functioning” is defined as “an intelligence quotient (I.Q.) of seventy (70) or below.” Id.
The evidence before this court strongly suggests that Bowling is not mentally retarded. Thus, Bowling does not make a prima facie showing on his claim of mental retardation such that he can receive permission to file a second or successive habeas petition.
Bowling has had four I.Q. tests — two were taken while he was in grade school and the other two were taken in preparation for his trial. While Bowling was in seventh grade (1966-67 academic year), he received scores of 74 and 79 on these tests. He was tested again twice in 1990, with both tests administered within a month of his December 1990 trial. He received a score of 86 using the WAIS-R test and a score of 87 on the Shipley Hartford Intelligence Scale.. None of these scores are at or below the cutoff of 70 established by Kentucky law as proof of significant subav-erage intellectual functioning. Further, in a separate case, the Kentucky Supreme Court determined that I.Q. scores of 74 and 78, similar to two of Bowling’s scores, “are 4 to 8 points respectively higher than the definition of a seriously mentally retarded offender” who would be ineligible for the death penalty. Woodall v. Commonwealth, 63 S.W.3d 104, 116 (Ky.2002).
Bowling argues that this court should not consider the absolute scores on these I.Q. tests, but instead apply a five-point margin of error. The five-point margin of error does place one of Bowling’s seventh-grade scores below the statutory cutoff. However, Bowling does not justify the five-point margin of error with any explanation nor does the margin of error appear to derive from any particular source. In addition, there is no indication that the psychologists who administered the I.Q. tests to Bowling would not have already considered the adequacy and accuracy of the testing mechanisms in calculating his scores or in using these instruments for evaluation in the first place. See United States v. Roane, 378 F.3d 382, 409 (4th Cir.2004) (in rejecting the argument that defendant’s I.Q. score should be considered within the range for those with mental retardation because of I.Q. score variations, the court observed that the psychologist’s care in calculating a score “belies the suggestion that [the psy*438chologist’s] analysis did not account for possible variations in his testing instrument”). Finally, the I.Q. scores on the tests taken around the time of Bowling’s trial were 86 and 87, scores that are significantly higher than the Kentucky statutory cutoff of 70 even taking into account Bowling’s suggested five-point margin of error.
Bowling also argues that his academic performance indicates that he is mentally retarded. According to Bowling, his “grades were deplorable-mostly D’s and F’s,” and he “was recommended for special education as early as the first grade, failed the second grade, and dropped out of school after spending nearly three years in the ninth grade.” It is true that Bowling failed the ninth grade three times before leaving school. However, the record reflects that, between the third and sixth grades, Bowling received mostly C’s and did not fail a class. School records do not indicate that Bowling ever took special education classes. In addition, a teacher commented during Bowling’s eighth-grade year that “[t]his child is a slow learner; however, if a genuine interest is taken in him, he will perform and behave more satisfactorily. With guidance, his potential as a student will improve.” Thus, while Bowling’s academic performance was not exceptional, it does not follow from the evidence before this court that he is mentally retarded.
Bowling also presents the affidavits of his mother, sister, and son to establish that he was deficient in adaptive skills and unable to function in the basic aspects of everyday life. Iva Lee Bowling, his mother, stated that Bowling was slow in learning to walk and in becoming toilet trained, that he had scarlet fever when he was three years old, and that he had multiple head injuries as an infant and a teenager. She also stated that Bowling wandered off as a child and teenager, got into fights, and was a follower. According to his mother, he had problems with money, difficulty in keeping jobs, and difficulty maintaining personal relationships. Patricia Gentry, Bowling’s sister, and Thomas Jason Bowling, Bowling’s son, reiterated these and similar observations.
These limitations do not state a prima facie case for Bowling’s mental retardation claim. Bowling’s known, diagnosed psychological problems include attention deficit hyperactivity disorder, alcohol abuse, and a personality disorder. These diagnoses provide an explanation for the various problems noted by Bowling’s mother and sister. While some of the problems may also be indicative of a low level of intellectual functioning, their existence has little tendency to establish mental retardation, given Bowling’s other diagnoses and the fact that the psychological evidence is inconsistent with mental retardation.
Most damaging to Bowling’s claim that he is mentally retarded are the results of evaluations conducted by the two psychologists who examined him before the trial. Dr. Smith, the court-appointed psychologist who evaluated Bowling over two days and through a variety of psychological instruments, concluded that “T.C. is not mentally retarded.” He diagnosed Bowling as suffering from alcohol abuse, personality disorder, and attention deficit hyperactivity disorder. Bowling’s attorneys also retained a psychologist, Dr. Beal. Dr. Beal did not specifically indicate whether or not he thought Bowling is mentally retarded. However, he did find that Bowling’s level of intellectual functioning fell “in the low average range of intellectual functioning.” He also diagnosed Bowling as suffering from major depression, personality disorder, and alcohol abuse, but these disorders “were not of such severity to cause him to be substantially impaired in *439his ability to know the wrongfulness of the acts alleged.”
Bowling’s claim that he is mentally retarded must also be considered in context. Bowling raised this argument for the first time in the months preceding his execution date, after the Supreme Court declined to review his first habeas petition. Yet, Kentucky law has prohibited the execution of the seriously mentally retarded since 1990, before his case went to trial. Additionally, Penry v. Lynaugh, while not categorically prohibiting execution of the mentally retarded, held that “the jury must be able to consider and give effect to any mitigating evidence relevant to a defendant’s background,” including evidence that the defendant is mentally retarded. 492 U.S. 302, 328, 109 S.Ct. 2934, 106 L.Ed.2d 256 (1989). The evidence Bowling presents to this court was also available well before his trial, as it consists mainly of his family’s observations, school records, and I.Q. tests administered in the seventh grade and before trial. If Bowling is in fact mentally retarded, he likely would not have waited fourteen years to present this argument only in connection with a request for a second or successive habeas petition.
While Atkins did create a new rule prohibiting the execution of the mentally retarded, it does not appear that its mandate affected Kentucky law in particular, because Kentucky already prohibited the imposition of this sentence on the “seriously mentally retarded.” Further, the test enunciated in Atkins for defining who is mentally retarded, see 536 U.S. at 308 n. 3, 122 S.Ct. 2242, is remarkably similar to the Kentucky statute; both require significantly subaverage intellectual functioning, limitations in adaptive functioning, and an onset before adulthood. Thus, Atkins did not significantly alter Bowling’s ability to present his claim that he is mentally retarded under Kentucky law.
Under either Kentucky law or Atkins, Bowling has failed to establish a prima facie case on his mental retardation claim. None of his I.Q. scores falls below the cutoff of 70 established by the Kentucky statute. Evidence that he has limitations in functioning does not show that he is mentally retarded; rather, these limitations are just as indicative of the other psychological disorders from which he suffers as they are of low level intellectual functioning. Thus, we deny Bowling’s application.
III.
Bowling also appeals from a federal district court order denying his motion to reopen his first habeas corpus proceeding. Bowling’s Rule 60(b) motion asserts two general claims. First, Bowling argues that his ineffective-assistance-of-counsel claim should be reopened because of new evidence in the form of a Brooklyn Law Review article that he suggests indicates that the jury did not consider the mitigation evidence presented at trial. He also claims that the intervening Supreme Court decision in Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003), provides that it is not inconsistent for a defendant to both assert his own innocence and present mitigating evidence. Second, Bowling contends that his Brady claim should be reopened based upon the intervening Supreme Court decision in Banks v. Dretke, 540 U.S. 668, 124 S.Ct. 1256, 157 L.Ed.2d 1166 (2004), and because the prosecution allegedly committed fraud on the court by failing to reveal exculpatory evidence.
The district court initially construed Bowling’s motion as a second or successive habeas corpus petition, which cannot be filed in the district court without prior authorization from a federal court of appeals. See 28 U.S.C. § 2244(b)(3)(A). *440Rather than transferring the case to this court for consideration, however, the district court alternatively held that Bowling did not satisfy his burden under Rule 60(b) and denied the motion. The district court declined to grant a certificate of appeala-bility. Bowling now requests a certificate of appealability from this court.
In Gonzalez v. Crosby, — U.S. -, 125 S.Ct. 2641, 162 L.Ed.2d 480 (2005), the Supreme Court explained how to differentiate a true Rule 60(b) motion from an unauthorized second or successive habeas corpus petition. The Supreme Court explained that a movant presents a “claim” under 28 U.S.C. § 2244 if the motion “attacks the federal court’s previous resolution of a claim on the merits, since alleging that the court erred in denying habeas relief on the merits is effectively indistinguishable from alleging that the movant is, under the substantive provisions of the statutes, entitled to habeas relief.” Id. at 2648. By contrast, it held that such a “claim” is not present in a true Rule 60(b) motion, which instead “attacks, not the substance of the federal court’s resolution of a claim on the merits, but some defect in the integrity of the federal habeas proceedings.” Id.
We hold that the district court properly determined that Bowling’s Rule 60(b) motion was in fact a second or successive habeas petition under Gonzalez. However, the district court failed to comply with its obligation to transfer the case to this court. See In re Sims, 111 F.3d 45, 47 (6th Cir.1997). Thus, we construe Bowling’s Rule 60(b) motion as an application for permission to file a second or successive habeas petition. Bowling is not entitled to file a successive habeas petition because he seeks to re-litigate claims previously raised in his initial habeas petition, which is not permitted under 28 U.S.C. § 2244(b)(1). Further, his claims are without merit and thus do not justify granting leave to file a second or successive petition for habeas corpus.
IV.
For the foregoing reasons, we deny both of Bowling’s applications for an order authorizing a federal district court to consider his second or successive petition for a writ of habeas corpus.