563528 · 13563528 - 1
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important PrimePages database: 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:
|Description:||563528 · 13563528 - 1|
|Verification status (*):||Proven|
|Official Comment (*):||Generalized Woodall|
|Unofficial Comments:||This prime has 1 user comment below.|
|Proof-code(s): (*):||p262 : Vogel, Gcwsieve, MultiSieve, PrimeGrid, OpenPFGW|
|Decimal Digits:||627745 (log10 is 627744.02035427)|
|Rank (*):||3153 (digit rank is 1)|
|Entrance Rank (*):||65|
|Currently on list? (*):||short|
|Submitted:||12/8/2009 10:18:57 CDT|
|Last modified:||12/11/2009 05:50:21 CDT|
|Score (*):||45.2038 (normalized score 1.7946)|
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.
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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 91121 person_id 9 machine RedHat P4 P4 what prime notes Command: /home/caldwell/client/pfgw -tp -q"563528*13^563528-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 563528*13^563528-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(262144,19) to FFT(262144,18) Reduced from FFT(262144,18) to FFT(262144,17) Reduced from FFT(262144,17) to FFT(262144,16) 4170658 bit request FFT size=(262144,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 563528*13^563528-1 is prime! (-156.0986s+0.1500s) [Elapsed time: 2.80 days] modified 2020-07-07 17:30:36 created 2009-12-08 10:23:01 id 111617
field value prime_id 91121 person_id 9 machine Ditto P4 P4 what trial_divided notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 563528 13 563528 -1 2>&1 [Elapsed time: 9.545 seconds] modified 2020-07-07 17:30:36 created 2009-12-08 10:35:12 id 111619