2840178 · Bern(1870)/85

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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:	2840178 · Bern(1870)/85
Verification status (*):	PRP
Official Comment (*):	Irregular, ECPP
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	3821 (log₁₀ is 3820.47675595)
Rank (*):	94683 (digit rank is 1)
Entrance Rank (*):	32314
Currently on list? (*):	yes
Submitted:	12/3/2003 02:49:03 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	67526
Status Flags:	Verify
Score (*):	29.4528 (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 178452, tag last modified 2023-03-11 16:02:31)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 686
Subcategory: "ECPP"
(archival tag id 178453, tag last modified 2024-12-16 19:37:11)

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 67526

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 2997477656...5776579313 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1012270 Running N-1 test using base 3 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) 25392 bit request FFT size=(1536,17) Running N+1 test using discriminant 11, base 1+sqrt(11) 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) 25400 bit request FFT size=(1536,17) Calling N+1 BLS with factored part 0.23% and helper 0.09% (0.77% proof) 2997477656...5776579313 is Fermat and Lucas PRP! (11.0226s+0.0018s)

modified 2020-07-07 22:30:47

created 2003-12-03 02:53:02

id 72462

field	value
prime_id	67526
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 2997477656...5776579313 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1012270 Running N-1 test using base 3 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) 25392 bit request FFT size=(1536,17) Running N+1 test using discriminant 11, base 1+sqrt(11) 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) 25400 bit request FFT size=(1536,17) Calling N+1 BLS with factored part 0.23% and helper 0.09% (0.77% proof) 2997477656...5776579313 is Fermat and Lucas PRP! (11.0226s+0.0018s)
modified	2020-07-07 22:30:47
created	2003-12-03 02:53:02
id	72462

Query times: 0.0003 seconds to select prime, 0.0004 seconds to seek comments.