96880162584451340130465 · 2352601 + 1
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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:96880162584451340130465 · 2352601 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):p106 : Smith_Robert, Carmody, Ksieve, Racers, OpenPFGW
Decimal Digits:106167   (log10 is 106166.46373597)
Rank (*):37590 (digit rank is 1)
Entrance Rank (*):2917
Currently on list? (*):no
Submitted:10/30/2007 07:19:02 CDT
Last modified:10/30/2007 07:50:41 CDT
Removed (*):1/24/2009 06:11:18 CDT
Database id:82797
Status Flags:none
Score (*):39.7386 (normalized score 0.0182)

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_id82797
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/pfgw -o -f -q"96880162584451340130465*2^352601+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
9688016258...1340130465*2^352601+1 1/1


trial factoring to 36337923
9688016258...1340130465*2^352601+1 has no small factor.
[Elapsed time: 258.804 seconds]
modified2011-12-27 16:48:49
created2007-10-30 07:22:02
id94708

fieldvalue
prime_id82797
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"96880162584451340130465*2^352601+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 9688016258...1340130465*2^352601+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 23
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)
705364 bit request FFT size=(49152,16)
Calling Brillhart-Lehmer-Selfridge with factored part 99.98%
9688016258...1340130465*2^352601+1 is prime! (1577.8800s+0.0000s)
[Elapsed time: 27.63 minutes]
modified2008-01-03 10:54:43
created2007-10-30 07:23:03
id94709

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.