(((((((((((((133556228506830452012 - 5983)2/4 - 763)2/4 - 4639)2/4 - 5699)2/4 - 35519)2/4 - 82547)2/4 - 8476499)2/4 - 1678383)2/4 - 34308675)2/4 - 652040831)2/4 - 5471199)2/4 - 6254699427)2/4 - 17186947797)/4

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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:(((((((((((((133556228506830452012 - 5983)2/4 - 763)2/4 - 4639)2/4 - 5699)2/4 - 35519)2/4 - 82547)2/4 - 8476499)2/4 - 1678383)2/4 - 34308675)2/4 - 652040831)2/4 - 5471199)2/4 - 6254699427)2/4 - 17186947797)/4
Verification status (*):PRP
Official Comment (*):[none]
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p269 : Zhou, OpenPFGW
Decimal Digits:154212   (log10 is 154211.40296379)
Rank (*):44604 (digit rank is 1)
Entrance Rank (*):4961
Currently on list? (*):no
Submitted:6/13/2010 00:33:40 UTC
Last modified:3/11/2023 15:54:10 UTC
Removed (*):6/14/2010 22:19:07 UTC
Database id:93175
Status Flags:Verify
Score (*):40.8882 (normalized score 0.0039)

User comments about this prime (disclaimer):

User comments are allowed to convey mathematical information about this number, how it was proven prime.... See our guidelines and restrictions.

Lei Zhou writes (11 Sep 2014):  (report abuse)
The certification of primality is here: http://bitc.bme.emory.edu/~lzhou/blogs/?p=132

This prime number is the 20th term of the proving chain p(k+1)=p(k)*(p(k)-m)+/-1:
INDEX m +/-1 p
0 - - 2
1 1 + 3
2 1 - 5
3 1 - 19
4 7 - 227
5 3 + 50849
6 29 - 2584146179
7 19 - 6677811425341522639
8 77 - (13355622850683045201^2-5933)/4
9 25 - ((13355622850683045201^2-5983)^2/4-629)/4
10 67 - (((13355622850683045201^2-5983)^2/4-763)^2/4-4493)/4
11 73 + ((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5325)/4
12 187 + (((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-34965)/4
13 277 + ((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-76725)/4
14 2911 + (((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-82547)^2/4-8473917)/4
15 1291 + ((((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-82547)^2/4-8476499)^2/4-1666677)/4
16 5853 + (((((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-82547)^2/4-8476499)^2/4-1678383)^2/4-34257605)/4
17 25535 + ((((((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-82547)^2/4-8476499)^2/4-1678383)^2/4-34308675)^2/4-652036221)/4
18 2305 - (((((((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-82547)^2/4-8476499)^2/4-1678383)^2/4-34308675)^2/4-652040831)^2/4-5313029)/4
19 79085 - ((((((((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-82547)^2/4-8476499)^2/4-1678383)^2/4-34308675)^2/4-652040831)^2/4-5471199)^2/4-6254437229)/4
20 131099 + (((((((((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-82547)^2/4-8476499)^2/4-1678383)^2/4-34308675)^2/4-652040831)^2/4-5471199)^2/4-6254699427)^2/4-17186947797)/4

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.
fieldvalue
prime_id93175
person_id9
machineDitto P4 P4
whattrial_divided
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] (((((((((((((133556228506.........99427)^2/4-17186 1/1 trial factoring to 54121136 (((((((((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-82547)^2/4-8476499)^2/4-1678383)^2/4-34308675)^2/4-652040831)^2/4-5471199)^2/4-6254699427)^2/4-17186947797)/4 has no small factor. [Elapsed time: 620.710 seconds]
modified2020-07-07 22:30:34
created2010-06-13 00:35:01
id115732

fieldvalue
prime_id93175
person_id9
machineDitto P4 P4
whatprp
notesPFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (((((((((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-82547)^2/4-8476499)^2/4-1678383)^2/4-34308675)^2/4-652040831)^2/4-5471199)^2/4-6254699427)^2/4-17186947797)/4 [N-1/N+1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1024568 bit request FFT size=(65536,16) Running N+1 test using discriminant 5, base 5+sqrt(5) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(65536,20) to FFT(65536,19) Reduced from FFT(65536,19) to FFT(65536,18) Reduced from FFT(65536,18) to FFT(65536,17) Reduced from FFT(65536,17) to FFT(65536,16) 1024576 bit request FFT size=(65536,16) Calling N-1 BLS with factored part 0.00% and helper 0.00% (0.01% proof) (((((((((((((13355622850683045201^2-5983)^2/4-763)^2/4-4639)^2/4-5699)^2/4-35519)^2/4-82547)^2/4-8476499)^2/4-1678383)^2/4-34308675)^2/4-652040831)^2/4-5471199)^2/4-6254699427)^2/4-17186947797)/4 is Fermat and Lucas PRP! (-1255.8192s+0.0300s) [Elapsed time: 4.45 hours]
modified2020-07-07 22:30:34
created2010-06-16 08:44:12
id115836

Query times: 0.0004 seconds to select prime, 0.0005 seconds to seek comments.
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