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π( x) for x up to 100,000,000,000,000,000.
At this site we maintain a list of the 5000 Largest Known Primes which is updated hourly. This list is the most important databases at The Prime Pages: 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:
field (help)  value 
Description:  2 · 3^{1074726} + 1 
Verification status (*):  Proven 
Official Comment:  
Unofficial Comments:  This prime has 1 user comment below. 
Proofcode(s): (*):  p199 : Broadhurst, NewPGen, OpenPFGW 
Decimal Digits:  512775 (log_{10} is 512774.91862984) 
Rank (*):  1399 (digit rank is 1) 
Entrance Rank (*):  91 
Currently on list? (*):  yes 
Submitted:  2/13/2010 07:52:58 CDT 
Last modified:  2/17/2010 07:50:50 CDT 
Database id:  91746 
Status Flags:  none 
Score (*):  44.5826 (normalized score 2.3488) 

User comments about this prime (disclaimer):
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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  91746 
person_id  9 
machine  Ditto P4 P4 
what  trial_divided 
notes  Command: /home/ditto/client/TrialDiv/TrialDiv q 2 3 1074726 1 2>&1 [Elapsed time: 10.060 seconds]

modified  20111227 16:48:40 
created  20100213 08:05:02 
id  112868 

field  value 
prime_id  91746 
person_id  9 
machine  RedHat P4 P4 
what  prime 
notes  Command: /home/caldwell/client/pfgw t q"2*3^1074726+1" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing 2*3^1074726+1 [N1, BrillhartLehmerSelfridge] Running N1 test using base 2 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N1 test using base 17 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N1 test using base 23 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N1 test using base 29 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N1 test using base 31 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Running N1 test using base 41 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(229376,19) to FFT(229376,18) Reduced from FFT(229376,18) to FFT(229376,17) Reduced from FFT(229376,17) to FFT(229376,16) 3406812 bit request FFT size=(229376,16) Calling BrillhartLehmerSelfridge with factored part 100.00% 2*3^1074726+1 is prime! (1665.4337s+0.1400s) [Elapsed time: 4.00 days]

modified  20100313 18:56:30 
created  20100213 07:53:01 
id  112867 

Query times: 0.0004 seconds to select prime, 0.0008 seconds to seek comments.
