(290124116 - 1)2 - 2
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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:(290124116 - 1)2 - 2
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):p403 : Bonath, Cksieve, OpenPFGW
Decimal Digits:611246   (log10 is 611245.979814454)
Rank (*):1692 (digit rank is 1)
Entrance Rank (*):1465
Currently on list? (*):short
Submitted:3/1/2019 09:32:08 CDT
Last modified:3/2/2019 20:50:24 CDT
Database id:126269
Status Flags:TrialDiv
Score (*):45.122 (normalized score 2.9135)

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_id126269
person_id9
machineUsing: Xeon (pool) 4c+4c 3.5GHz
whatprime
notesCommand: /home/caldwell/clientpool/1/pfgw64 -tc -q"(290^124116-1)^2-2" 2>&1
PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing (290^124116-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 3
Running N-1 test using base 13
Running N-1 test using base 23
Running N-1 test using base 31
Running N-1 test using base 37
Running N-1 test using base 53
Running N-1 test using base 59
Running N+1 test using discriminant 103, base 2+sqrt(103)
Running N+1 test using discriminant 103, base 3+sqrt(103)
Calling N+1 BLS with factored part 50.00% and helper 0.00% (150.00% proof)


(290^124116-1)^2-2 is prime! (126660.2253s+0.0179s)
[Elapsed time: 35.18 hours]
modified2019-03-02 20:44:02
created2019-03-01 09:33:01
id171947

Query times: 0.0005 seconds to select prime, 0.0007 seconds to seek comments.