1105 · 21314586 + 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:1105 · 21314586 + 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L2139 : Hagerty, PSieve, Srsieve, PrimeGrid, LLR
Decimal Digits:395733   (log10 is 395732.86124221)
Rank (*):6402 (digit rank is 1)
Entrance Rank (*):616
Currently on list? (*):no
Submitted:2/10/2012 19:14:17 CDT
Last modified:2/10/2012 20:50:25 CDT
Removed (*):2/7/2018 06:03:50 CDT
Database id:104518
Status Flags:none
Score (*):43.7866 (normalized score 0.8096)

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_id104518
person_id9
machineRedHat P4 P4
whattrial_divided
notesCommand: /home/caldwell/client/TrialDiv/TrialDiv -q 1105 2 1314586 1 2>&1
[Elapsed time: 9.981 seconds]
modified2012-02-19 19:07:47
created2012-02-10 19:18:02
id138601

fieldvalue
prime_id104518
person_id9
machineRedHat P4 P4
whatprime
notesCommand: /home/caldwell/client/pfgw -t -q"1105*2^1314586+1" 2>&1
PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5]
Primality testing 1105*2^1314586+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
1105*2^1314586+1 is prime! (4121.6877s+0.0011s)
[Elapsed time: 68.70 minutes]
modified2012-02-19 19:07:47
created2012-02-10 19:23:01
id138613

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