(2102435 + 1)2 - 2

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:(2102435 + 1)2 - 2
Verification status (*):Proven
Official Comment (*):[none]
Proof-code(s): (*):p126 : Minovic, MultiSieve, OpenPFGW
Decimal Digits:61673   (log10 is 61672.01521168)
Rank (*):51923 (digit rank is 1)
Entrance Rank (*):1222
Currently on list? (*):no
Submitted:2/23/2004 06:57:27 CDT
Last modified:2/23/2004 06:57:27 CDT
Removed (*):11/17/2005 15:58:38 CDT
Database id:68943
Status Flags:none
Score (*):38.0643 (normalized score 0.0016)

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_id68943
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -f -tc -q"(2^102435+1)^2-2" 2>&1 PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4] Primality testing (2^102435+1)^2-2 [N-1/N+1, Brillhart-Lehmer-Selfridge] trial factoring to 20329733 Running N-1 test using base 3 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409750 bit request FFT size=(28672,16) Running N-1 test using base 7 Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409750 bit request FFT size=(28672,16) Running N+1 test using discriminant 17, base 1+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409758 bit request FFT size=(28672,16) Running N+1 test using discriminant 17, base 2+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409758 bit request FFT size=(28672,16) Running N+1 test using discriminant 17, base 3+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409758 bit request FFT size=(28672,16) Running N+1 test using discriminant 17, base 4+sqrt(17) Using SSE2 FFT Adjusting authentication level by 1 for PRIMALITY PROOF Reduced from FFT(28672,20) to FFT(28672,19) Reduced from FFT(28672,19) to FFT(28672,18) Reduced from FFT(28672,18) to FFT(28672,17) Reduced from FFT(28672,17) to FFT(28672,16) 409758 bit request FFT size=(28672,16) Calling N+1 BLS with factored part 50.00% and helper 0.01% (150.01% proof) (2^102435+1)^2-2 is prime! (-871.0246s+0.0000s)
modified2020-07-07 17:30:46
created2004-02-23 07:23:01
id73895

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