3119 · 2518613 + 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:3119 · 2518613 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):L1396 : Vandaele, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:156122   (log10 is 156121.56315666)
Rank (*):36778 (digit rank is 1)
Entrance Rank (*):4798
Currently on list? (*):no
Submitted:6/24/2010 17:30:25 CDT
Last modified:6/24/2010 19:57:04 CDT
Removed (*):7/10/2010 14:19:13 CDT
Database id:93294
Status Flags:none
Score (*):40.9261 (normalized score 0.0248)

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.

Pascal Vandaele writes (11 Sep 2014):  (report abuse)
Divides xGF(518611,9,8).

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.
machineDitto P4 P4
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 3119 2 518613 1 2>&1 [Elapsed time: 9.994 seconds]
modified2020-07-07 17:30:34
created2010-06-24 17:35:02

machineDitto P4 P4
notesCommand: /home/ditto/client/pfgw -t -q"3119*2^518613+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3119*2^518613+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1037258 bit request FFT size=(65536,16) Calling Brillhart-Lehmer-Selfridge with factored part 100.00% 3119*2^518613+1 is prime! (1426.5500s+0.0000s) [Elapsed time: 24.15 minutes]
modified2020-07-07 17:30:34
created2010-06-24 17:45:15

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.
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