"41769334305470218025...(102088 other digits)...13913798335329393079"

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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:	"41769334305470218025...(102088 other digits)...13913798335329393079"
Verification status (*):	Proven
Official Comment (*):	[none]
Proof-code(s): (*):	p62 : Underwood, PrimeForm_egroup, OpenPFGW
Decimal Digits:	102128 (log₁₀ is 102127.620858)
Rank (*):	47989 (digit rank is 2)
Entrance Rank (*):	1060
Currently on list? (*):	no
Submitted:	5/26/2005 20:23:54 UTC
Last modified:	3/11/2023 15:54:10 UTC
Removed (*):	8/4/2008 17:50:09 UTC
Database id:	74612
Blob database id:	137
Status Flags:	none
Score (*):	39.6191 (normalized score 0.0046)

Description: (from blob table id=137)

This number is
49334180280 * (RSA200)^512 - 1
where RSA200 is the 200 - digit RSA factorization challenge number:
2799783391 1221327870 8294676387 2260162107 0446786955 4285375600 0992932612 8400107609 3456710529 5536085606 1822351910 9513657886 3710595448 2006576775 0985805576 1357909873 4950144178 8631789462 9518723786 9221823983
F. Bahr, M. Boehm, J. Franke, T. Kleinjung, plus P. Montgomery, H. te Riele, and about 75 cpu years of calculation found this number is the product of the following two primes:
3532461934 4027701212 7260497819 8464368671 1974001976 2502364930 3468776121 2536794232 0005854795 6528088349
and
7925869954 4783330333 4708584148 0059687737 9758573642 1996073433 0341455767 8728181521 3538140930 4740185467

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 74612

person_id 9

machine Linux P4 2.8GHz

what prime

notes PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4176933430...5329393079 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper trial factoring to 34863399 Running N-1 test using base 13 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 678530 bit request FFT size=(49152,16) Running N+1 test using discriminant 31, base 1+sqrt(31) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 678538 bit request FFT size=(49152,16) Running N+1 test using discriminant 31, base 2+sqrt(31) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 678538 bit request FFT size=(49152,16) Calling N+1 BLS with factored part 100.00% and helper 0.00% (300.00% proof) 4176933430...5329393079 is prime! (-1698.6792s+0.3100s) Helper File: 35324619344027701212726049781984643...(100 digits)...76121253679423200058547956528088349 79258699544783330333470858414800596...(100 digits)...55767872818152135381409304740185467

modified 2020-07-07 22:30:43

created 2005-06-03 16:42:20

id 79722

field	value
prime_id	74612
person_id	9
machine	Linux P4 2.8GHz
what	prime
notes	PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 4176933430...5329393079 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file helper trial factoring to 34863399 Running N-1 test using base 13 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 678530 bit request FFT size=(49152,16) Running N+1 test using discriminant 31, base 1+sqrt(31) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 678538 bit request FFT size=(49152,16) Running N+1 test using discriminant 31, base 2+sqrt(31) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(49152,20) to FFT(49152,19) Reduced from FFT(49152,19) to FFT(49152,18) Reduced from FFT(49152,18) to FFT(49152,17) Reduced from FFT(49152,17) to FFT(49152,16) 678538 bit request FFT size=(49152,16) Calling N+1 BLS with factored part 100.00% and helper 0.00% (300.00% proof) 4176933430...5329393079 is prime! (-1698.6792s+0.3100s) Helper File: 35324619344027701212726049781984643...(100 digits)...76121253679423200058547956528088349 79258699544783330333470858414800596...(100 digits)...55767872818152135381409304740185467
modified	2020-07-07 22:30:43
created	2005-06-03 16:42:20
id	79722

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