- 197676570 · 18851280661 · Bern(1836)/(59789 · 3927024469727)

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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.

Description:	- 197676570 · 18851280661 · Bern(1836)/(59789 · 3927024469727)
Verification status (*):	PRP
Official Comment (*):	Irregular, ECPP
Unofficial Comments:	This prime has 1 user comment below.
Proof-code(s): (*):	c8 : Water, Broadhurst, Primo
Decimal Digits:	3734 (log₁₀ is 3733.18001478)
Rank (*):	88440 (digit rank is 1)
Entrance Rank (*):	32180
Currently on list? (*):	short
Submitted:	11/20/2003 09:03:29 CDT
Last modified:	11/20/2003 09:03:29 CDT
Database id:	67302
Status Flags:	Verify
Score (*):	29.3809 (normalized score 0)

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.

Irregular Primes (archivable *)
Prime on list: yes, rank 20
Subcategory: "Irregular Primes"
(archival tag id 178331, tag last modified 2021-05-01 12:20:47)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 548
Subcategory: "ECPP"
(archival tag id 178332, tag last modified 2021-05-04 10:20:37)

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)

certificate

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 67302

person_id 9

machine Linux P4 2.8GHz

what prp

notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 1513612772...3522251053 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 987133 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24812 bit request FFT size=(1536,17) Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24812 bit request FFT size=(1536,17) Running N-1 test using base 19 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24812 bit request FFT size=(1536,17) Running N+1 test using discriminant 29, base 3+sqrt(29) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24820 bit request FFT size=(1536,17) Calling N-1 BLS with factored part 0.25% and helper 0.10% (0.86% proof) 1513612772...3522251053 is Fermat and Lucas PRP! (14.5559s+0.0017s)

modified 2020-07-07 17:30:47

created 2003-11-20 09:19:05

id 72235

field	value
prime_id	67302
person_id	9
machine	Linux P4 2.8GHz
what	prp
notes	PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 1513612772...3522251053 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 987133 Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24812 bit request FFT size=(1536,17) Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24812 bit request FFT size=(1536,17) Running N-1 test using base 19 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24812 bit request FFT size=(1536,17) Running N+1 test using discriminant 29, base 3+sqrt(29) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1536,21) to FFT(1536,20) Reduced from FFT(1536,20) to FFT(1536,19) Reduced from FFT(1536,19) to FFT(1536,18) Reduced from FFT(1536,18) to FFT(1536,17) 24820 bit request FFT size=(1536,17) Calling N-1 BLS with factored part 0.25% and helper 0.10% (0.86% proof) 1513612772...3522251053 is Fermat and Lucas PRP! (14.5559s+0.0017s)
modified	2020-07-07 17:30:47
created	2003-11-20 09:19:05
id	72235

Query times: 0.0005 seconds to select prime, 0.006 seconds to seek comments.