276474 · Bern(2030)/469951697500688159155

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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:	276474 · Bern(2030)/469951697500688159155
Verification status (*):	PRP
Official Comment (*):	Irregular, ECPP
Proof-code(s): (*):	c8 : Broadhurst, Water, Primo
Decimal Digits:	4200 (log₁₀ is 4199.41751278)
Rank (*):	94112 (digit rank is 1)
Entrance Rank (*):	32131
Currently on list? (*):	yes
Submitted:	12/29/2003 22:33:51 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	67877
Status Flags:	Verify
Score (*):	29.7468 (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 18
Subcategory: "Irregular Primes"
(archival tag id 195543, tag last modified 2023-03-11 16:02:31)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 648
Subcategory: "ECPP"
(archival tag id 195544, tag last modified 2024-10-27 10:37:10)

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 67877

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 2615247426...9372647907 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1121927 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) 27910 bit request FFT size=(1536,19) Running N+1 test using discriminant 5, base 1+sqrt(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) 27918 bit request FFT size=(1536,19) Running N+1 test using discriminant 5, base 2+sqrt(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) 27918 bit request FFT size=(1536,19) Running N+1 test using discriminant 5, base 4+sqrt(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) 27918 bit request FFT size=(1536,19) Calling N+1 BLS with factored part 0.17% and helper 0.16% (0.69% proof) 2615247426...9372647907 is Fermat and Lucas PRP! (43.4884s+0.0020s)

modified 2020-07-07 22:30:47

created 2003-12-29 22:53:03

id 72816

field	value
prime_id	67877
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 2615247426...9372647907 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1121927 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) 27910 bit request FFT size=(1536,19) Running N+1 test using discriminant 5, base 1+sqrt(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) 27918 bit request FFT size=(1536,19) Running N+1 test using discriminant 5, base 2+sqrt(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) 27918 bit request FFT size=(1536,19) Running N+1 test using discriminant 5, base 4+sqrt(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) 27918 bit request FFT size=(1536,19) Calling N+1 BLS with factored part 0.17% and helper 0.16% (0.69% proof) 2615247426...9372647907 is Fermat and Lucas PRP! (43.4884s+0.0020s)
modified	2020-07-07 22:30:47
created	2003-12-29 22:53:03
id	72816

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