"15238445279350815802...(398164 other digits)...70851559196354845061"

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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 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:	"15238445279350815802...(398164 other digits)...70851559196354845061"
Verification status (*):	Proven
Official Comment (*):	[none]
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	p44 : Broadhurst, OpenPFGW
Decimal Digits:	398204 (log₁₀ is 398203.18294066)
Rank (*):	14109 (digit rank is 1)
Entrance Rank (*):	931
Currently on list? (*):	no
Submitted:	2/12/2013 01:34:56 UTC
Last modified:	3/11/2023 15:54:10 UTC
Removed (*):	2/18/2018 22:16:26 UTC
Database id:	111195
Blob database id:	288
Status Flags:	none
Score (*):	43.8057 (normalized score 0.3076)

Description: (from blob table id=288)

[This prime has a pre-calculated decimal expansion (linked blob)]

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

David Broadhurst writes (11 Sep 2014): (report abuse)

Prime of the form N = x^2 + x + 41 = 1 mod 163^90000. The Pari-GP code for N is as follows: {D=163; n=90000; M=D^n; B=truncate(sqrt(4-D+O(D^n))); X=50942*M-(B+1)/2; N=X^2+X+41;}

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.

field value

prime_id 111195

person_id 9

machine Ditto P4 P4

what trial_divided

notes Command: /home/ditto/client/pfgw -o -f p_111195.txt 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 1523844527935081....1559196354845061 1/1 mro=0 trial factoring to 148535086 1523844527...6354845061 has no small factor. [Elapsed time: 19835.626 seconds]

modified 2020-07-07 22:30:23

created 2013-02-12 01:35:02

id 152659

field	value
prime_id	111195
person_id	9
machine	Ditto P4 P4
what	trial_divided
notes	Command: /home/ditto/client/pfgw -o -f p_111195.txt 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] 1523844527935081....1559196354845061 1/1 mro=0 trial factoring to 148535086 1523844527...6354845061 has no small factor. [Elapsed time: 19835.626 seconds]
modified	2020-07-07 22:30:23
created	2013-02-12 01:35:02
id	152659

field value

prime_id 111195

person_id 9

machine RedHat P4 P4

what prime

notes Command: /home/caldwell/client/pfgw -tc p_111195.txt 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 1523844527...6354845061 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 13 Running N-1 test using base 17 Running N+1 test using discriminant 29, base 4+sqrt(29) Calling N-1 BLS with factored part 50.00% and helper 0.00% (150.00% proof) 1523844527...6354845061 is prime! (170852.0052s+6.1847s) [Elapsed time: 1.98 days]

modified 2020-07-07 22:30:23

created 2013-02-12 02:05:18

id 152661

field	value
prime_id	111195
person_id	9
machine	RedHat P4 P4
what	prime
notes	Command: /home/caldwell/client/pfgw -tc p_111195.txt 2>&1 PFGW Version 3.4.5.32BIT.20110215.x86_Dev [GWNUM 26.5] Primality testing 1523844527...6354845061 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Running N-1 test using base 13 Running N-1 test using base 17 Running N+1 test using discriminant 29, base 4+sqrt(29) Calling N-1 BLS with factored part 50.00% and helper 0.00% (150.00% proof) 1523844527...6354845061 is prime! (170852.0052s+6.1847s) [Elapsed time: 1.98 days]
modified	2020-07-07 22:30:23
created	2013-02-12 02:05:18
id	152661

Query times: 0.0002 seconds to select prime, 0.0003 seconds to seek comments.