Prime Number Money Prizes

Several organizations offer cash prizes for the discovery of large prime numbers. The largest prizes are the Cooperative Computing Awards of the Electronic Frontier Foundation (EFF), four prizes tied to decimal digit thresholds and ranging from $50,000 to $250,000. Two have been claimed, both by volunteers of the Great Internet Mersenne Prime Search (GIMPS). GIMPS offers smaller standing awards of its own, and bounties have been attached to related problems in computational number theory, including integer factorization.

The EFF Cooperative Computing Awards

The EFF announced the Cooperative Computing Awards in 1999, with the stated purpose of encouraging ordinary internet users to pool idle computing capacity against problems requiring massive computation. John Gilmore, an EFF co-founder, led the project. The prize fund is a single earmarked donation from an individual supporter rather than money drawn from membership dues or general revenue. When the awards were announced, the largest known prime had 909,526 digits.

Four prizes were defined, each payable to the first individual or group to find a prime at or above a given number of decimal digits. A discovery can qualify for only one prize, and receives the largest one still available. If a billion-digit prime were found before any hundred-million-digit prime, it would claim the $250,000 award while the $150,000 award remained open.

Conditions of a claim

The rules place several requirements on a claimant. The date and time of discovery must be given and all hardware and software disclosed in full. The primality proof must be deterministic, so a probabilistic certification does not suffice on its own. The discovery and proof must be published in a refereed academic journal, and the EFF reserves the right to require additional verification by independent experts. The 2008 discovery appeared in the Fibonacci Quarterly before the prize was presented. An EFF advisory panel assesses claims, chaired for many years by Landon Curt Noll, who held the largest known prime record himself in 1978 and 1979.

The million-digit award

In 1999 Nayan Hajratwala, an information technology consultant in Plymouth, Michigan, ran the GIMPS client Prime95 on an IBM Aptiva with a 350 MHz Intel Pentium II processor. After about 111 days of intermittent background computation the machine reported that 2^6,972,593 - 1, a number of 2,098,960 digits, was prime. It was the first prime of more than one million digits to be found. The EFF presented the award on 6 April 2000 at the Computers, Freedom and Privacy conference in Toronto, and GIMPS passed the entire sum to the discoverer.

The ten-million-digit award

On 23 August 2008 a computer in the mathematics department of the University of California, Los Angeles reported that 2^43,112,609 - 1, a number of 12,978,189 digits, was prime. It was the 45th known Mersenne prime and the first known to exceed ten million digits. Edson Smith, the department's computing manager, had installed the GIMPS software on otherwise idle laboratory machines. The EFF presented the award on 22 October 2009. GIMPS directed $50,000 to the UCLA mathematics department and $25,000 to charity, retaining the balance for project expenses.

GIMPS research discovery awards

GIMPS operates its own awards alongside the EFF prizes. A volunteer whose computer finds a new Mersenne prime of fewer than one hundred million digits, which is not large enough for either currently unclaimed EFF prize, receives $3,000. The 52nd known Mersenne prime, 2^136,279,841 - 1, found in October 2024 at 41,024,320 digits on a network of data centre graphics processors assembled by Luke Durant, fell into this category. GIMPS recorded credit for it jointly to Durant, Mihai Preda, George Woltman and Aaron Blosser, covering the software authors and the server maintainer as well as the volunteer.

Participants assign their interest in the hundred-million-digit EFF award to GIMPS, which has published in advance how the money would be divided. The $150,000 would be split into three equal parts: $50,000 to the discoverer, $50,000 to a mathematics-related charity with 501(c)(3) status chosen by GIMPS, and $50,000 retained for expenses and further awards. If two qualifying primes were found at nearly the same time, priority would go to the result first sent either to the PrimeNet server or directly to GIMPS by email.

Prospects for the hundred-million-digit award

The number of decimal digits in 2^p - 1 is ⌊p · log₁₀(2)⌋ + 1, so one hundred million digits requires an exponent of at least 332,192,807. Because that exponent must itself be prime, the smallest usable candidate is 332,192,831. A Lucas-Lehmer test on it performs p - 2 modular squarings, more than 332 million of them, each acting on a number of over 332 million bits. Work at that scale uses fast Fourier transform multiplication, increasingly on graphics processors. The 2024 record was the first GIMPS discovery made on data centre hardware rather than personal computers, produced on an Nvidia A100 in Dublin and confirmed on an H100 in San Antonio.

Other prizes related to prime numbers

• The Baillie-PSW-related bounty. Carl Pomerance, John Selfridge and Samuel Wagstaff have offered a standing prize of $620 for a composite number n congruent to 2 or 3 modulo 5 that is both a base-2 pseudoprime and a Fibonacci pseudoprime. These are the conditions in the published offer, which is commonly discussed in connection with the Baillie-PSW test. No qualifying composite has been found, and none exists below 2⁶⁴.
• The RSA Factoring Challenge. From 1991 to 2007 RSA Laboratories offered bounties of up to $200,000 for factoring specified semiprimes, the products of two large secret primes. The challenge drove work on factoring methods, notably the general number field sieve. Several of the numbers have been factored since the challenge was withdrawn, without payment.
• PrimeGrid. This distributed computing project searches for record primes of non-Mersenne forms, including Proth primes, generalized Fermat primes and Cullen and Woodall primes. It offers recognition and computational badges rather than cash.

Participation

GIMPS distributes client software without charge for Windows, Linux and macOS. Prime95 runs on general purpose processors, while GpuOwl, written by Mihai Preda and later extended by George Woltman, runs on graphics processors; CUDALucas and mfaktc have also been used. Registration on the PrimeNet server at mersenne.org records exponent assignments and credit for any discovery.

Explore More Prime Number Topics

• A Very Large Prime Number: the largest known primes and how they were found.
• Different Types of Prime Numbers: Mersenne, Fermat and Proth primes.
• How to Check Whether a Number Is Prime: primality tests and algorithms in detail.
• The Illegal Prime Number: how primes intersect with software code and copyright law.
• Prime Number Check: test an integer of up to 20,000 digits with our online checker.