(6³⁸⁶⁶⁰ - 1)² - 2

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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:	(6³⁸⁶⁶⁰ - 1)² - 2
Verification status (*):	Proven
Official Comment (*):	[none]
Proof-code(s): (*):	p13 : Ballinger, OpenPFGW
Decimal Digits:	60167 (log₁₀ is 60166.654679663)
Rank (*):	57565 (digit rank is 1)
Entrance Rank (*):	1428
Currently on list? (*):	no
Submitted:	2/20/2004 02:39:14 UTC
Last modified:	3/11/2023 15:54:10 UTC
Removed (*):	7/31/2005 18:02:56 UTC
Database id:	68904
Status Flags:	none
Score (*):	37.9881 (normalized score 0.0009)

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 68904

person_id 9

machine Linux P4 2.8GHz

what prime

notes Command: /home/caldwell/client/pfgw -f -tc -q"(6^38660-1)^2-2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (6^38660-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 19798896 Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(24576,20) to FFT(24576,19) Reduced from FFT(24576,19) to FFT(24576,18) Reduced from FFT(24576,18) to FFT(24576,17) 399748 bit request FFT size=(24576,17) Running N+1 test using discriminant 11, base 2+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(24576,20) to FFT(24576,19) Reduced from FFT(24576,19) to FFT(24576,18) Reduced from FFT(24576,18) to FFT(24576,17) 399756 bit request FFT size=(24576,17) Running N+1 test using discriminant 11, base 3+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(24576,20) to FFT(24576,19) Reduced from FFT(24576,19) to FFT(24576,18) Reduced from FFT(24576,18) to FFT(24576,17) 399756 bit request FFT size=(24576,17) Calling N+1 BLS with factored part 50.01% and helper 0.01% (150.05% proof) (6^38660-1)^2-2 is prime! (-789.4173s+0.0100s)

modified 2020-07-07 22:30:46

created 2004-02-20 02:53:01

id 73857

field	value
prime_id	68904
person_id	9
machine	Linux P4 2.8GHz
what	prime
notes	Command: /home/caldwell/client/pfgw -f -tc -q"(6^38660-1)^2-2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (6^38660-1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 19798896 Running N-1 test using base 5 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(24576,20) to FFT(24576,19) Reduced from FFT(24576,19) to FFT(24576,18) Reduced from FFT(24576,18) to FFT(24576,17) 399748 bit request FFT size=(24576,17) Running N+1 test using discriminant 11, base 2+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(24576,20) to FFT(24576,19) Reduced from FFT(24576,19) to FFT(24576,18) Reduced from FFT(24576,18) to FFT(24576,17) 399756 bit request FFT size=(24576,17) Running N+1 test using discriminant 11, base 3+sqrt(11) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(24576,20) to FFT(24576,19) Reduced from FFT(24576,19) to FFT(24576,18) Reduced from FFT(24576,18) to FFT(24576,17) 399756 bit request FFT size=(24576,17) Calling N+1 BLS with factored part 50.01% and helper 0.01% (150.05% proof) (6^38660-1)^2-2 is prime! (-789.4173s+0.0100s)
modified	2020-07-07 22:30:46
created	2004-02-20 02:53:01
id	73857

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

(638660 - 1)2 - 2

This prime's information:

Verification data:

(6³⁸⁶⁶⁰ - 1)² - 2