E(1736)/13510337079405137518589526468536905

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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:	E(1736)/13510337079405137518589526468536905
Verification status (*):	PRP
Official Comment (*):	Euler irregular, ECPP
Proof-code(s): (*):	c4 : Broadhurst, Primo
Decimal Digits:	4498 (log₁₀ is 4497.45211785)
Rank (*):	93647 (digit rank is 1)
Entrance Rank (*):	31911
Currently on list? (*):	yes
Submitted:	1/11/2004 03:55:03 UTC
Last modified:	3/11/2023 15:54:10 UTC
Database id:	68041
Blob database id:	106
Status Flags:	Verify
Score (*):	29.96 (normalized score 0)

Description: (from blob table id=106)

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

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.

Euler Irregular primes (archivable *)
Prime on list: yes, rank 15
Subcategory: "Euler Irregular primes"
(archival tag id 195422, tag last modified 2023-10-06 17:37:13)
Elliptic Curve Primality Proof (archivable *)
Prime on list: no, rank 610
Subcategory: "ECPP"
(archival tag id 195423, 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 68041

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 2832160403...7135736289 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1208717 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 29890 bit request FFT size=(1792,17) Running N+1 test using discriminant 17, base 8+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 29898 bit request FFT size=(1792,17) Running N+1 test using discriminant 17, base 10+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 29898 bit request FFT size=(1792,17) Calling N+1 BLS with factored part 0.19% and helper 0.15% (0.74% proof) 2832160403...7135736289 is Fermat and Lucas PRP! (54.5075s+0.0022s)

modified 2020-07-07 22:30:46

created 2004-01-16 17:27:23

id 73298

field	value
prime_id	68041
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 2832160403...7135736289 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 1208717 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 29890 bit request FFT size=(1792,17) Running N+1 test using discriminant 17, base 8+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 29898 bit request FFT size=(1792,17) Running N+1 test using discriminant 17, base 10+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(1792,21) to FFT(1792,20) Reduced from FFT(1792,20) to FFT(1792,19) Reduced from FFT(1792,19) to FFT(1792,18) Reduced from FFT(1792,18) to FFT(1792,17) 29898 bit request FFT size=(1792,17) Calling N+1 BLS with factored part 0.19% and helper 0.15% (0.74% proof) 2832160403...7135736289 is Fermat and Lucas PRP! (54.5075s+0.0022s)
modified	2020-07-07 22:30:46
created	2004-01-16 17:27:23
id	73298

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