(1284991359 · 298305 + 1) · (96060285 · 2135170 + 1) - 2
(Another of the Prime Pages' resources)
The Largest Known Primes Icon
  View this page in:   language help
 

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:(1284991359 · 298305 + 1) · (96060285 · 2135170 + 1) - 2
Verification status (*):Proven
Official Comment:
Unofficial Comments:This prime has 1 user comment below.
Proof-code(s): (*):p180 : Andersen, Fleuren, PrimeForm_egroup, OpenPFGW
Decimal Digits:70301   (log10 is 70300.0696817261)
Rank (*):46501 (digit rank is 1)
Entrance Rank (*):3344
Currently on list? (*):no
Submitted:10/7/2005 16:31:44 CDT
Last modified:10/10/2005 06:54:21 CDT
Removed (*):6/10/2006 17:17:18 CDT
Database id:75857
Status Flags:none
Score (*):38.4681 (normalized score 0.0043)

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.

Chris Caldwell writes (11 Sep 2014): 
PrimeForm e-group found this (then) largest known Chen prime in October 2005. See the e-mail to the PrimForm list. Wikipedia defines "A prime number p is called a Chen prime if p+2 is either a prime or a semiprime [a product of two primes]. The first few Chen primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 47, 53, 59, 67, 71, 83, 89, 101 (sequence A109611 in OEIS)"

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_id75857
person_id9
machineLinux P4 2.8GHz
whatprime
notesCommand: /home/caldwell/client/pfgw -f -tc -q"(1284991359*2^98305+1)*(96060285*2^135170+1)-2" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing (1284991359*2^98305+1)*(96060285*2^135170+1)-2 [N-1/N+1, Brillhart-Lehmer-Selfridge]
trial factoring to 23387879
Running N-1 test using base 5
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)
467072 bit request FFT size=(28672,17)
Running N+1 test using discriminant 11, base 2+sqrt(11)
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)
467080 bit request FFT size=(28672,17)
Running N+1 test using discriminant 11, base 3+sqrt(11)
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)
467080 bit request FFT size=(28672,17)
Running N+1 test using discriminant 11, base 4+sqrt(11)
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)
467080 bit request FFT size=(28672,17)
Calling N+1 BLS with factored part 42.13% and helper 0.02% (126.42% proof)
(1284991359*2^98305+1)*(96060285*2^135170+1)-2 is prime! (12649.4555s+0.0217s)
[Elapsed time: 12650 seconds]
modified2005-10-19 12:27:07
created2005-10-08 05:05:39
id81051

Query times: 0.0004 seconds to select prime, 0.0007 seconds to seek comments.