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: U(5989, 1, 3169)-U(5989, 1, 3168) Verification status (*): Proven Official Comment: Lehmer number Unofficial Comments: This prime has 1 user comment below. Proof-code(s): (*): x25 : Water, Broadhurst, Primo, OpenPFGW Decimal Digits: 11967   (log10 is 11966.658352983) Rank (*): 42886 (digit rank is 1) Entrance Rank (*): 27814 Currently on list? (*): short Submitted: 7/14/2005 04:02:26 CDT Last modified: 7/14/2005 04:02:26 CDT Database id: 75050 Status Flags: none Score (*): 32.9964 (normalized score 0.0004)

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.

Lehmer number (archivable *)

Prime on list: yes, rank 20
Subcategory: "Lehmer number"
(archival tag id 193928, tag last modified 2009-02-12 20:01:29)

User comments about this prime (disclaimer):

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David Broadhurst writes (26 Nov 2005): 

BLS proof with BLS helper primV(5989,1,1584)

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 75050 person_id 9 machine Linux P4 2.8GHz what prime notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4553580126...6142465921 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file b6337.fac trial factoring to 3488421 Running N-1 test using base 19 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(5120,21) to FFT(5120,20) Reduced from FFT(5120,20) to FFT(5120,19) Reduced from FFT(5120,19) to FFT(5120,18) Reduced from FFT(5120,18) to FFT(5120,17) Reduced from FFT(5120,17) to FFT(5120,16) 79514 bit request FFT size=(5120,16) Running N-1 test using base 29 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(5120,21) to FFT(5120,20) Reduced from FFT(5120,20) to FFT(5120,19) Reduced from FFT(5120,19) to FFT(5120,18) Reduced from FFT(5120,18) to FFT(5120,17) Reduced from FFT(5120,17) to FFT(5120,16) 79514 bit request FFT size=(5120,16) Running N+1 test using discriminant 43, base 9+sqrt(43) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(5120,21) to FFT(5120,20) Reduced from FFT(5120,20) to FFT(5120,19) Reduced from FFT(5120,19) to FFT(5120,18) Reduced from FFT(5120,18) to FFT(5120,17) Reduced from FFT(5120,17) to FFT(5120,16) 79522 bit request FFT size=(5120,16) Calling N+1 BLS with factored part 31.14% and helper 9.87% (103.29% proof) 4553580126...6142465921 is prime! (141.6138s+0.0078s) Helper File: 2 2 2 2 2 2 2 3 3 5 7 11 11 13 17 23 37 47 53 71 83 89 107 113 179 193 197 199 263 353 499 599 829 1409 1511 1847 2113 2593 3167 3169 3433 4799 5987 6337 8353 14717 16193 18217 19249 35279 35999 95071 117811 209311 356831 365179 454213 562357 638177 675179 2414779 3513007 5124017 12282073 21542161 27257221 30232259 74968343 132679693 337505191 524628983 687635167 784902959 1182343579 1591162649 1772503127 2359973089 3995239247 5167998289 10604573893 16141944719 16154381231 17868856921 214814158703 8184816170123 28373688569249 42302630756159 49284584706059 125592338664803 148738039104029 12411625431889553 37568166238581527 101756998780571327 434927028366384247 1832535680934450241 9213381276597687390959 481758368219718626707969 5597283002876306960259637333 17607859096822669984053980737 2712911617746825785227517360989548239 49156456689746083892320515236204020353469 86461817321218426234861002599203993683173894785799 7097109581964724570488775561698813406325056250998982172383 363728305312543820703367896098766343246812969210657526850600053539697 40834457419073605804784649376388477...(91 digits)...54294932248918934188084199925466653 97868391647465861434926897735158826...(96 digits)...80051934444500957659172984848953069 26389871660351645415751458954607132...(99 digits)...16117628703427931201308939900899161 2 577 8641 304831 3617153 8157007 150619967 195148799 17753431495828607 36175630846581285823 7392555275158716634687 primV(5989,1,1584) modified 2005-12-30 08:30:42 created 2005-07-15 09:42:40 id 80166