EFF has already received and rejected dozens of incorrect or deficient claims. Please read and follow all of the rules before submitting a claim. Please note especially:
There is no award available for the discovery of a mathematical technique, algorithm, or theorem. We will not offer a payment or reward for the discovery of a mathematical technique, unless that technique is used to determine a specific prime number in compliance with all the other rules below. New discoveries in number theory or other branches of mathematics should be directed to an appropriate forum, but we are unable to provide any reward for them or any evaluation of their merits.
There is no award available for merely knowing how to find or test for large prime numbers. Methods for finding large prime numbers have been known for many years; however, all known methods require substantial amounts of computer time (years of computation on current hardware). Our awards require that you find a particular prime number, not simply know a way to find prime numbers. We already have well-proven and well-understood computer programs capable of finding prime numbers -- they just take too long to work. Thus, a computer program that would eventually find or verify prime numbers is not, by itself, sufficient to qualify for an award.
There is no award available for a secret proof or discovery. The rules require open publication of a discovery, and this publication must be made prior to the submission of a claim. EFF does not derive any commercial benefit from improvements in number theory and is specifically interested in promoting open publication of research.
This set of awards is intended to spur collaborative computing. In the past, large computations (including factoring and primality testing) have been successfully carried out by teams working together over the Internet to pool their computational resources. These awards are intended to promote the development of this method of performing computations. We consider it unlikely that these awards can be won by an isolated individual without access to specialized equipment or signifiant computing resources; for decades, the discovery of world-record primes has required the use of supercomputers or Internet collaboration. We consider it unlikely that these awards can be won by mathematical reasoning alone without electronic computation.
The rules below will not be waived or varied. In particular, submissions that have not yet been validated by peer review will be rejected. EFF does not offer assistance in determining the correctness or incorrectness of a submission. EFF appreciates the creativity of researchers in trying to make progress in number theory and computer science, but asks that researchers respect the fact that our awards have a limited scope and purpose and will not be awarded for other kinds of work, however novel or useful.
- EFF establishes four computation awards
- EFF will award $50,000 to the first individual or group who discovers the
first prime number with at least 1,000,000 decimal digits.
[[NOTE: The $50,000 award was given out on Apr. 6, 2000]]
- EFF will award $100,000 to the first individual or group who discovers the
first prime number with at least 10,000,000 decimal digits.
- EFF will award $150,000 to the first individual or group who discovers the
first prime number with at least 100,000,000 decimal digits.
- EFF will award $250,000 to the first individual or group who discovers the
first prime number with at least 1,000,000,000 decimal digits.NOTE: Leading zeroes don't count!- Only one award will be given per discovery
Only one computation award will be granted per prime discovery. In a case where multiple awards apply, the larger award will be granted.
For example, if you happen to discover a prime with 1,000,000,000 or more decimal digits before the $150,000 award is claimed, you will be eligible for the $250,000 award only. Once an award is paid out, all other current and future claims become ineligible for that particular award.
All awards will be disbursed. If someone receives the $250,000 award for discovering a prime with a 1,000,000,000 or more digits and the $150,000 award has not yet been given out, whoever next discovers a prime with a 100,000,000 or more decimal digits will be eligible for the $150,000 award.
In the case where two or more valid claims for the same award are submitted, the valid claim with the earliest verifiable discovery date will be honored.
- The primality proof must be a deterministic proof for a distinct integer
The claim must be for the primality for a distinct integer. The proof of primality of that distinct integer must be constructive, definitive, reproductable, verifiable and deterministic.
Probable-primality proofs are not acceptable. Claims involving probable primes will not be accepted.
Your claim must explicitly identify a distinct prime number. For example, claims involving Mills' Theorem real number or Matijasevic polynomial without providing a specific solution will not be accepted.
- Full disclosure is required
In the interest of promoting the state of the art of computation, those receiving EFF Computation Awards must allow EFF to freely publish their methods, algorithms, source code, scripts and detailed descriptions of hardware without undue restrictions or costs. EFF's publication of this information is intended give others the opportunity to replicate the discovery, as well as to provide a foundation for improving on the results.
Proofs that are "for sale" are not acceptable. EFF will not consider proofs that are proprietary or that are encumbered with restrictions that get in the way of their unrestricted re-distribution.
- What to include in your submission
Your claim must have each the following 7 items. Please reference each of these 7 items in your claim:
- Your claim must indicate the value of the prime number by concise formula or decimal expansion.
The EFF reserves the right to require you to provide URL of the decimal expansion of the prime number.
- Your claim must include a description of the primality testing method used by those who are claiming the award. This must include the complete primality certificate, which includes all of the necessary information to evaluate and reconstruct the proof.
In other words, tell us:
- How did you prove primality?
- Did you use the Lucas-Lehmer test, the Proth's Theorem or Riesel test or some other method?
- Did you pre-screen potential candidates by eliminating values with small factors?
- Your claim must include a description of any hardware and software used in the primality test.
EFF reserves the right to require a more detailed disclosure. For example, EFF may require evidence that the hardware was used legally, with the owner's permission and support. References to well known hardware and software may be given.
- Your claim must indicate the amount of computation time, along with a breakdown by hardware type, that was used in the primality test.
- Your claim must provide the date and time in UTC (Coordinated Universal Time) of the discovery.
Tell us when you first proved the primality of the number that you are claiming.
- Your claim must include a citation and abstract of a published paper that announces the discovery and outlines the proof of primality. The cited paper must be published in a refereed academic journal with a peer review process that is approved by EFF.
We strongly recommend that you submit your paper to an appropriate refereed academic journal of one of the following societies:
- American Mathematical Society
- Australian Mathematical Society
- Canadian Mathematical Society
- London Mathematical Society
- Mathematical Association of America
Note that not all publications of the above societies are appropriate refereed academic journals. Questions about the appropriateness of a journal should be directed to the EFF computation award question address (see rule #9 below).
IMPORTANT: The EFF will reject any claim that fails to provide a citation and abstract of a published paper that announces the discovery and outlines the proof of primality.
- Your claim must provide a single point of contact, including an E-mail address, postal address and phone number where EFF can contact you regarding the claim. In the case of a group effort, you must select an individual with whom EFF will correspond. Providing a URL of a home page is encouraged but not required.
EFF reserves the right to require more information should it determine that the information supplied (either in the cited paper or directly as part of the claim) is unsubstantiated. EFF also reserves the right to require independent verification of any information supplied (see below).
- Verification of a claim
The EFF reserves the right to require a claim to be verified by independent experts of its choosing. Failure to fully cooperate the EFF selected experts will result in your claim being rejected.
- Lump sum payment will be made to a single point of contact
Should EFF grant an award, the award funds will be paid in a lump sum to an individual or organization as directed by the point of contact. It is the responsibility of the receiving individual or organization to pay any and all applicable taxes. In the case of a group discovery, it is the responsibility of the receiving individual or organization to distribute the award.
- EFF board is the final authority
The decisions of the EFF board of directors in granting or refusing a claim are final. EFF reserves the right to reject all claims by any individual or group which has previously submitted false or insufficient claims.
- Where to send claims
To make a claim, send an E-mail message containing the required information to:
coop-award-claim@eff.orgThe E-mail message must have a subject containing the following words in the following order:
cooperative prime number award claimIMPORTANT: Failure to use a proper subject in your claim related E-mail may result in your E-mail being ignored!
It is the responsibility of those claiming the award to ensure that the E-mail is sent in a timely way. EFF is not responsible for lost or delayed E-mail. The EFF is not responsible for claims that were ignored because the proper E-mail subject was not used.
- For more information about the awards
Questions about the EFF computation awards may be mailed to:
coop-award-question@eff.orgThe E-mail message must have a subject containing the following words in the following order:
cooperative prime number award questionPlease be sure to use the proper E-mail subject or your question(s) may be ignored!
Please do not use the above E-mail to ask questions about mathematics. Please do not use the above E-mail to ask us for help in finding or proving the primality of a number. For questions about mathematics, discovering prime numbers and computation, see:
- EFF Cooperative Computing Awards Home page
- Frequently Asked Questions about the awards
- Prime Number Resources and Information
In addition see any of the many Frequently Asked Questions (FAQs) available on the Web. Ideas and remarks on prime numbers and number theory should be posted to the appropriate newsgroup or sent to the appropriate refereed academic journal.
- Updates to the rules
The EFF reserves the right to make modifications to these rules in order to correct errors, remove ambiguity, and for clarification.
