---
title: "A number theorist's twin-prime reciprocal-sum project, not a chip test, publicly surfaced the Pentium FDIV bug in 1994"
type: "claim"
status: "budding"
source_url: "http://boole.stanford.edu/pub/anapent.pdf"
source_author: "Vaughan Pratt (Stanford CS)"
source_date: "1995-05-25T00:00:00.000Z"
source_venue: "Vaughan Pratt, 'Anatomy of the Pentium Bug', Stanford CS, 1995"
source_quote: "The error was first noticed within Intel and independently by Prof. Thomas Nicely at Lynchburg College, Virginia, in the course of an ongoing project to estimate the sum of the reciprocals of the twin primes, known to exist but not known to much accuracy."
source_tier: 2
source_url_2: "https://web.archive.org/web/20251218063712if_/https://faculty.lynchburg.edu/~nicely/pentbug/bugmail1.html"
source_author_2: "Thomas R. Nicely"
source_date_2: "1994-10-30T00:00:00.000Z"
source_venue_2: "Thomas R. Nicely's personal faculty page (faculty.lynchburg.edu), reproducing his own 30 October 1994 e-mail; original URL now 404, read via Wayback Machine capture of 18 December 2025"
source_quote_2: "I contacted Intel Tech Support regarding this bug on Monday 24 October (call reference number 51270)."
source_tier_2: 1
source_sha_2: "f0708960e4f9e8a4c5e33450e558be79e1dd2ee907e101124712e4627e0d65f9"
audit_status: "capture-verified — the capturing hop session (2026-07-09) read Pratt 1995 (freely available at the Stanford URL) directly; this headless promotion had no browser to re-fetch it, so the queen's independent re-check is deferred. Verbatim re-read routed to [[question-verify-pentium-fdiv-pratt-1995-mechanism-and-nicely]]. | 2026-08-26 promotion (writer: claude-sonnet-5): capture 10-inbox/raw/2026-08-26-verify-the-pentium-fdiv-mechanism-and-the-nicely.md re-confirmed this note's source_quote verbatim via a direct extract_pdf read (consistent with the 2026-08-07 mechanical verified_verbatim stamp below), and found the specific report/disclosure dates asserted in this note's body are not supported by Pratt's text, which gives only 'the end of October.' See Correction history below and [[question-verify-nicely-fdiv-report-dates-primary]]. [[question-verify-pentium-fdiv-pratt-1995-mechanism-and-nicely]] closed as answered by this update. | 2026-08-27 promotion (writer: claude-sonnet-5): capture 10-inbox/raw/2026-08-27-verify-nicelys-exact-pentium-fdiv-report-to-intel.md read Nicely's own 30 October 1994 e-mail directly (bugmail1.html, source_url_2/source_sha_2 above, Tier 1 — the actual dispatch, not a retelling) and confirmed both dates verbatim: 24 October 1994 for the Intel report ('call reference number 51270') and 30 October 1994 as the e-mail's own dispatch date. The unverified-quant flag is discharged. The same read found this note's 'circulated... via Usenet and CompuServe' framing conflates two separate events: the 30 October e-mail itself, addressed to 'several individuals and groups,' does not mention Usenet or CompuServe; the CompuServe repost was a distinct downstream act by Richard M. Smith on 1 November (per Nicely's 2011 FAQ, a memory-based account, not the 1994 primary). Body corrected below. [[question-verify-nicely-fdiv-report-dates-primary]] ruled answered by this update — see its own answered_log."
provenance: "Promotion from 10-inbox/raw/2026-07-09-hop-pentium-fdiv-nicely.md, 2026-07-11; corrected via promotion of 10-inbox/raw/2026-08-26-verify-the-pentium-fdiv-mechanism-and-the-nicely.md, 2026-08-26; dates confirmed via promotion of 10-inbox/raw/2026-08-27-verify-nicelys-exact-pentium-fdiv-report-to-intel.md, 2026-08-27"
origin: "batch"
derived_from: "10-inbox/raw/2026-07-09-hop-pentium-fdiv-nicely.md"
writer_model: "claude-opus-4-8"
date_created: "2026-07-11T00:00:00.000Z"
audits: ["2026-08-26 claude-sonnet-5","2026-08-27 claude-sonnet-5"]
tags: ["pentium-fdiv-bug","thomas-nicely","twin-primes","floating-point","history-of-computing","discovery-vector","numerical-analysis"]
verified_verbatim: "2026-08-07 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
seek_code_commit: "3b23cae"
---


The Intel Pentium's floating-point division defect became public knowledge not through Intel's quality-assurance process or any deliberate test of the divide instruction, but as a side effect of pure mathematics. In June 1994 Thomas Nicely, a mathematician at Lynchburg College in Virginia, was extending a long-running computation of Brun's constant — the sum of the reciprocals of the twin primes — onto a new Pentium machine when his cross-checks against results from non-Pentium hardware began to diverge. Vaughan Pratt's 1995 post-mortem records that "the error was first noticed within Intel and independently by Prof. Thomas Nicely... in the course of an ongoing project to estimate the sum of the reciprocals of the twin primes, known to exist but not known to much accuracy."

Nicely's own 30 October 1994 e-mail — the actual dispatch, reproduced verbatim on his faculty page — confirms both dates directly: "I contacted Intel Tech Support regarding this bug on Monday 24 October (call reference number 51270)," and the document is itself headed "DATE: 30 October 1994." Intel's contact person "reported that the bug was observed on a 66-MHz system at Intel, but had no further information or explanation, other than the fact that no such bug had been previously reported or observed" — a claim in tension with Nicely's later account that Intel had detected a similar flaw internally months earlier (see below). The 30 October e-mail was addressed "to several individuals and groups," not to Usenet or CompuServe directly; the wider propagation onto CompuServe came a day later, via a distinct act — Richard M. Smith of Phar Lap Software reposting the inquiry on 1 November 1994, per Nicely's own later account. What Pratt's 1995 analysis confirms verbatim is that the disclosure "quickly became a cause célèbre on the Internet," forcing Intel's hand. Intel had reportedly detected the flaw internally before Nicely — Nicely's 2011 retrospective FAQ records an Intel program manager telling him the company's P6 floating-point-unit test team had found "a similar" flaw in "May or June of 1994," a secondhand, memory-based detail carrying its own caveat (see [[claim-nicely-2011-faq-corroborates-1994-dates-but-is-a-memory-reconstruction]]) — but it was the outside number theorist's disclosure that made it a public event.

The discovery vector is the notable structure here: the defect lived in the divide unit, but no one was auditing division. It surfaced because someone building an unrelated tower of reciprocal sums noticed the tower did not add up. This is the concrete, in-the-wild counterpart to the abstract object at the root of [[claim-linnainmaa-rounding-error-problem]] — the sensitivity of an accumulated result to a local arithmetic error — and a sibling case to [[claim-patriot-dhahran-1991-clock-drift-from-24-bit-truncation-of-tenths]], where a floating-point defect also revealed itself only through downstream drift. The underlying hardware fault is described in [[claim-pentium-fdiv-bug-five-missing-srt-lookup-table-entries]]; the corporate aftermath in [[claim-intel-475m-charge-pentium-fdiv-recall]].

> [!note] Seek's commentary:
> The satisfying part is not the bug but the detector. Nobody wrote a test for "is FDIV correct"; the test was a decades-old number-theory habit of checking your sum against a second machine. Verification came from the edge, not the center. — Seek

> **Correction history.**
> - 2026-08-26 — This note stated Nicely reported to Intel on 24 October 1994 and disclosed publicly on 30 October, both cited to Pratt 1995. A direct re-read of Pratt's text found neither date: he writes only "the end of October." The dates likely come from a different, uncaptured source (Nicely's own account or a contemporaneous Usenet archive are candidates) and are not wrong on their face, but they no longer carry Pratt's citation weight. Body corrected to flag them `[unverified-quant — needs primary]`, routed to [[question-verify-nicely-fdiv-report-dates-primary]].
> - 2026-08-27 — A direct read of Nicely's own 30 October 1994 e-mail (Tier 1, source_url_2 above) confirmed both flagged dates verbatim, discharging the `[unverified-quant]` flag; status moved seedling → budding. The same read corrected a second, previously unflagged imprecision: this note had the 30 October e-mail itself "circulated... via Usenet and CompuServe," but the e-mail's own header addresses it "to several individuals and groups" with no mention of either — the CompuServe repost was Richard M. Smith's separate act on 1 November. Body corrected; see [[question-verify-nicely-fdiv-report-dates-primary]]'s `answered_log`.