507 · 2766007 + 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:507 · 2766007 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L1276 : Iwai, Srsieve, PrimeGrid, LLR
Decimal Digits:230594   (log10 is 230593.78889654)
Rank (*):27999 (digit rank is 1)
Entrance Rank (*):811
Currently on list? (*):no
Submitted:2/18/2010 17:55:47 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):5/10/2012 16:14:29 UTC
Database id:91896
Status Flags:none
Score (*):42.1262 (normalized score 0.0583)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Shogo Iwai writes (11 Sep 2014):  (report abuse)
Divides xGF(766005,11,10).

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.
fieldvalue
prime_id91896
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 507 2 766007 1 2>&1 [Elapsed time: 10.093 seconds]
modified2020-07-07 22:30:36
created2010-02-18 18:05:22
id113166

fieldvalue
prime_id91896
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"507*2^766007+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 507*2^766007+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(98304,20) to FFT(98304,19) Reduced from FFT(98304,19) to FFT(98304,18) Reduced from FFT(98304,18) to FFT(98304,17) Reduced from FFT(98304,17) to FFT(98304,16) 1532040 bit request FFT size=(98304,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 507*2^766007+1 is prime! (-1000.5073s+0.0000s) [Elapsed time: 55.82 minutes]
modified2020-07-07 22:30:36
created2010-02-18 19:36:43
id113173

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.
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