Since the records established with the multiprocessor versions of ECPP (see ECPP records), there are no more attempts to certify big numbers with Primo. As a consequence, the cumbersome code part of Primo, specific to very big numbers, was suppressed. Primo can no more certify numbers having more than 10,000 bits (i.e., about 3000 decimal digits).

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Primo is a primality proving program based on the ECPP (Elliptic Curve Primality Proving) algorithm. Given positive odd integers, it tests whether these integers are prime, and if they are it produces primality certificates. With PRIMO, one can check crypto-primes and prove whether they are actually prime... or not.

A short description of the ECPP algorithm can be found at Elliptic Curve Primality Proving by Eric Weisstein (from MathWorld — A Wolfram Web Resource) and about all the theoretical background is in the numerous papers written by François Morain (see his page at LIX).

Executable for use under Win XP on 32-bit processors

In addition to primality certificates, Primo generates task reports that allow to quickly see which integers were certified or not. The following report was produced while processing (for certification) a list of four 1024-bit random pseudoprime integers.

[PRIMO - Task Report]
Version=3.0.6
WebSite=http://www.ellipsa.net/
Task=Certification
ID=B2FE7043B539A
Created=04/27/2008 00:00:00 AM

[Common]
Path=C:\primo\bench\1024\
Selected=4
Processed=4
Certified=4
Candidate #1=Certified, 5.99s
Candidate #2=Certified, 7.25s
Candidate #3=Certified, 6.95s
Candidate #4=Certified, 5.58s

[Candidate #1]
Input=prime01.in
Output=primo-B2FE7043B539A-001.out  <See Certificate> 
Status=Candidate certified prime

[Candidate #2]
Input=prime02.in
Output=primo-B2FE7043B539A-002.out
Status=Candidate certified prime

[Candidate #3]
Input=prime03.in
Output=primo-B2FE7043B539A-003.out
Status=Candidate certified prime

[Candidate #4]
Input=prime04.in
Output=primo-B2FE7043B539A-004.out
Status=Candidate certified prime

• Added a [Comments] section to input and output files.
• Fixed an incoherence reported by Norman Luhn (when verifying a certificate, if there was an expression in the [Candidate] section, Primo did not check whether this expression was equal to the candidate value).
• Miscellaneous insignificant improvements.

• Fixed a bug. Under rare circumstances, Primo could "forget" to delete some temporary files.
• Bigger discriminant tables. The 5 tables contain more than 870,000 discriminants.

• This version cannot certify integers having more than 10,000 bits.
• Use of 5 discriminant tables. These tables contain more than 760,000 discriminants.

• Fixed a bug that could lead to the internal error 2.15.2. Thanks to Wolfgang Ehrhardt who reported it.

• Use of new class invariants. Thanks to Michael Scott who kindly computed the needed modular functions.

• Installation problem fixed. Thanks to Sergey Lopatin who reported it.

• Backtrack tuning modified.
• Faster elliptic curve computations. The elliptic curve point multiplication is on average 10% faster.
• Certificate format modified. The new certificates are more compact, possibly up to 30% for the biggest ones.
• Certification reports added. Among other things, these reports contain the R values of backtracked tests (if any).

• New interface.
• New input file format.
  Expressions like N=10^700 + 7 are allowed.
• New certificate format.
• Automatic backtrack
• Verification and signature of certificates.
• The certifications are done in two phases: The 1st phase consists in finding a sequence of pseudoprimes. The 2nd phase consists in factoring class polynomials and computing elliptic curves and points.
• During the 1st phase, the work in progress is automatically saved every 10 minutes.
• It is possible (and easy) to resume an aborted certification.