94892254795 · 10103294 + 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:94892254795 · 10103294 + 1
Verification status (*):Proven
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p97 : Andersen, OpenPFGW
Decimal Digits:103305   (log10 is 103304.97723077)
Rank (*):47806 (digit rank is 1)
Entrance Rank (*):3190
Currently on list? (*):no
Submitted:9/9/2007 23:55:34 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):11/4/2008 18:28:20 UTC
Database id:82167
Status Flags:none
Score (*):39.6544 (normalized score 0.0047)

User comments about this prime (disclaimer):

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Jens Kruse Andersen writes (11 Sep 2014):  (report abuse)
The square of this prime, (94892254795*10103294+1)2 = 9004540020079200492025*10206588 + 189784509590*10103294+1, contains the same digits as its equally sized prime factors, making it the largest known prime vampire number as of 2007.

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.
machineRedHat P4 P4
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 94892254795 10 103294 1 2>&1 [Elapsed time: 9.028 seconds]
modified2020-07-07 22:30:40
created2007-09-10 00:22:02

machineRedHat P4 P4
notesCommand: /home/caldwell/client/pfgw -t -q"94892254795*10^103294+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 94892254795*10^103294+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(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 686352 bit request FFT size=(49152,16) Calling Brillhart-Lehmer-Selfridge with factored part 69.89% 94892254795*10^103294+1 is prime! (1518.3900s+0.0100s) [Elapsed time: 25.68 minutes]
modified2020-07-07 22:30:40
created2007-09-10 00:23:01

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.
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