"37776284510606367370...(1318 other digits)...89215663672079155201"

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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:	"37776284510606367370...(1318 other digits)...89215663672079155201"
Verification status (*):	Proven
Official Comment (*):	17-Carmichael factor (17)
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	p44 : Broadhurst, OpenPFGW
Decimal Digits:	1358 (log₁₀ is 1357.57721924)
Rank (*):	111365 (digit rank is 7)
Entrance Rank (*):	48072
Currently on list? (*):	no
Submitted:	5/16/2004 20:41:53 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	70373
Blob database id:	114
Status Flags:	none
Score (*):	26.2278 (normalized score 0)

Description: (from blob table id=114)

30251171081182250440877719388659053133527814231147715110662028434709116708107536039266669408375473553525482210304 * 1234578514375589600139299461309891215472748486893861616781823576745550941638810434994756075634238711959503055472046080 * 127265758603053652854671144842647200096979469577422603773338025370475153 * 2477# + 1

Archival tags:

There are certain forms classed as archivable: these prime may (at times) remain on this list even if they do not make the Top 5000 proper. Such primes are tracked with archival tags.

n-Carmichael factor (tolerated *)
Prime on list: no, rank 1
Subcategory: "17-Carmichael factor (17)"
(archival tag id 180342, tag last modified 2023-03-11 15:53:59)

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)

GP proof

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 70373

person_id 9

machine Linux P4 2.8GHz

what prime

notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3777628451...2079155201 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 326995 Running N-1 test using base 2503 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 9028 bit request FFT size=(512,18) Running N-1 test using base 2549 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 9028 bit request FFT size=(512,18) Running N-1 test using base 2557 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 9028 bit request FFT size=(512,18) Running N+1 test using discriminant 2609, base 96+sqrt(2609) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 9036 bit request FFT size=(512,18) Calling N-1 BLS with factored part 84.87% and helper 0.02% (254.67% proof) 3777628451...2079155201 is prime! (8.6092s+0.0007s)

modified 2020-07-07 22:30:45

created 2004-06-02 19:56:27

id 75534

field	value
prime_id	70373
person_id	9
machine	Linux P4 2.8GHz
what	prime
notes	PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 3777628451...2079155201 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 326995 Running N-1 test using base 2503 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 9028 bit request FFT size=(512,18) Running N-1 test using base 2549 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 9028 bit request FFT size=(512,18) Running N-1 test using base 2557 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 9028 bit request FFT size=(512,18) Running N+1 test using discriminant 2609, base 96+sqrt(2609) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(512,22) to FFT(512,21) Reduced from FFT(512,21) to FFT(512,20) Reduced from FFT(512,20) to FFT(512,19) Reduced from FFT(512,19) to FFT(512,18) 9036 bit request FFT size=(512,18) Calling N-1 BLS with factored part 84.87% and helper 0.02% (254.67% proof) 3777628451...2079155201 is prime! (8.6092s+0.0007s)
modified	2020-07-07 22:30:45
created	2004-06-02 19:56:27
id	75534

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