At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: a collection of research, records and results all about prime numbers. This page summarizes our information about one of these primes.

This prime's information:

field (help) value Description: 4104082046 · 4799# + 5657 Verification status (*): PRP Official Comment: Quadruplet (3), ECPP Proof-code(s): (*): c18 : Luhn, Primo Decimal Digits: 2058   (log10 is 2057.83231714) Rank (*): 81941 (digit rank is 3) Entrance Rank (*): 45871 Currently on list? (*): no Submitted: 5/2/2005 09:08:47 CDT Last modified: 5/2/2005 09:08:47 CDT Database id: 74350 Status Flags: Verify Score (*): 27.526 (normalized score 0)

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper.  Such primes are tracked with archival tags.

Quadruplet (archivable class *)

Prime on list: no, rank 6
Subcategory: "Quadruplet (3)"
(archival tag id 181274, tag last modified 2013-04-14 17:50:32)

Elliptic Curve Primality Proof (archivable *)

Prime on list: no, rank 476
Subcategory: "ECPP"
(archival tag id 181273, tag last modified 2013-05-19 13:50:29)

Verification data:

The Top 5000 Primes is a list for proven primes only. In order to maintain the integrity of this list, we seek to verify the primality of all submissions.  We are currently unable to check all proofs (ECPP, KP, ...), but we will at least trial divide and PRP check every entry before it is included in the list.

field value prime_id 74350 person_id 9 machine Linux P4 2.8GHz what prp notes Command: /home/caldwell/client/pfgw -f -tc -q"4104082046*4799#+5657" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4104082046*4799#+5657 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 515576 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) 13680 bit request FFT size=(768,18) Running N+1 test using discriminant 5, base 5+sqrt(5) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) 13688 bit request FFT size=(768,18) Running N+1 test using discriminant 5, base 6+sqrt(5) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(768,22) to FFT(768,21) Reduced from FFT(768,21) to FFT(768,20) Reduced from FFT(768,20) to FFT(768,19) Reduced from FFT(768,19) to FFT(768,18) 13688 bit request FFT size=(768,18) Calling N-1 BLS with factored part 0.41% and helper 0.18% (1.43% proof) 4104082046*4799#+5657 is Fermat and Lucas PRP! (4.9436s+0.0006s) modified 2005-05-06 13:13:57 created 2005-05-02 10:40:14 id 79378