113156 · 5110873 + 1
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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

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:113156 · 5110873 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):p203 : Petat, Srsieve, SierpinskiRiesel, PRP, OpenPFGW
Decimal Digits:77502   (log10 is 77501.954968335)
Rank (*):46405 (digit rank is 1)
Entrance Rank (*):4590
Currently on list? (*):no
Submitted:10/3/2006 11:50:06 CDT
Last modified:10/3/2006 12:20:18 CDT
Removed (*):12/26/2006 06:00:36 CDT
Database id:78602
Status Flags:none
Score (*):38.7688 (normalized score 0.0051)

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_id78602
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 113156 5 110873 1 2>&1
[Elapsed time: 8.457 seconds]
modified2007-03-03 21:00:43
created2006-10-03 11:52:01
id86301

fieldvalue
prime_id78602
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"113156*5^110873+1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 113156*5^110873+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 2
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(32768,20) to FFT(32768,19)
Reduced from FFT(32768,19) to FFT(32768,18)
Reduced from FFT(32768,18) to FFT(32768,17)
Reduced from FFT(32768,17) to FFT(32768,16)
514920 bit request FFT size=(32768,16)
Calling Brillhart-Lehmer-Selfridge with factored part 99.99%
113156*5^110873+1 is prime! (642.4900s+0.0100s)
[Elapsed time: 655 seconds]
modified2007-03-03 21:00:43
created2006-10-03 11:53:01
id86302

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