8 · 202¹⁵⁵⁷⁷¹ - 1

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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:	8 · 202¹⁵⁵⁷⁷¹ - 1
Verification status (*):	Proven
Official Comment (*):	[none]
Proof-code(s): (*):	p258 : Batalov, Srsieve, CRUS, OpenPFGW
Decimal Digits:	359108 (log₁₀ is 359107.79126006)
Rank (*):	14154 (digit rank is 1)
Entrance Rank (*):	246
Currently on list? (*):	no
Submitted:	7/22/2010 21:25:57 CDT
Last modified:	7/23/2010 19:20:31 CDT
Removed (*):	11/11/2014 13:15:57 CDT
Database id:	93684
Status Flags:	none
Score (*):	43.4881 (normalized score 0.3986)

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 93684

person_id 9

machine Ditto P4 P4

what trial_divided

notes Command: /home/ditto/client/TrialDiv/TrialDiv -q 8 202 155771 -1 2>&1 [Elapsed time: 9.134 seconds]

modified 2020-07-07 17:30:34

created 2010-07-22 21:35:02

id 116748

field	value
prime_id	93684
person_id	9
machine	Ditto P4 P4
what	trial_divided
notes	Command: /home/ditto/client/TrialDiv/TrialDiv -q 8 202 155771 -1 2>&1 [Elapsed time: 9.134 seconds]
modified	2020-07-07 17:30:34
created	2010-07-22 21:35:02
id	116748

field value

prime_id 93684

person_id 9

machine Ditto P4 P4

what prime

notes Command: /home/ditto/client/pfgw -tp -q"8*202^155771-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 8*202^155771-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(163840,20) to FFT(163840,19) Reduced from FFT(163840,19) to FFT(163840,18) Reduced from FFT(163840,18) to FFT(163840,17) Reduced from FFT(163840,17) to FFT(163840,16) 2385878 bit request FFT size=(163840,16) Calling Brillhart-Lehmer-Selfridge with factored part 86.94% 8*202^155771-1 is prime! (-1321.2513s+0.0700s) [Elapsed time: 21.27 hours]

modified 2020-07-07 17:30:34

created 2010-07-22 21:38:01

id 116749

field	value
prime_id	93684
person_id	9
machine	Ditto P4 P4
what	prime
notes	Command: /home/ditto/client/pfgw -tp -q"8202^155771-1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 8202^155771-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 3, base 1+sqrt(3) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(163840,20) to FFT(163840,19) Reduced from FFT(163840,19) to FFT(163840,18) Reduced from FFT(163840,18) to FFT(163840,17) Reduced from FFT(163840,17) to FFT(163840,16) 2385878 bit request FFT size=(163840,16) Calling Brillhart-Lehmer-Selfridge with factored part 86.94% 8*202^155771-1 is prime! (-1321.2513s+0.0700s) [Elapsed time: 21.27 hours]
modified	2020-07-07 17:30:34
created	2010-07-22 21:38:01
id	116749

Query times: 0.0004 seconds to select prime, 0.0006 seconds to seek comments.

8 · 202155771 - 1

Verification data:

8 · 202¹⁵⁵⁷⁷¹ - 1