266206 · 5608649 - 1
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The nth Prime Page will now find any of the first 2,623,557,157,654,233 primes or 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:266206 · 5608649 - 1
Verification status (*):Proven
Official Comment:
Proof-code(s): (*):L2050 : Kaiser1, Srsieve, PrimeGrid, SierpinskiRiesel, LLR
Decimal Digits:425433   (log10 is 425432.81938695)
Rank (*):2293 (digit rank is 1)
Entrance Rank (*):178
Currently on list? (*):yes
Submitted:2/10/2011 15:25:20 CDT
Last modified:2/14/2011 03:21:00 CDT
Database id:98188
Status Flags:none
Score (*):44.0089 (normalized score 1.3235)

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_id98188
person_id9
machineDitto P4 P4
whattrial_divided
notesCommand: /home/ditto/client/TrialDiv/TrialDiv -q 266206 5 608649 -1 2>&1
[Elapsed time: 9.822 seconds]
modified2011-12-27 16:48:34
created2011-02-10 15:35:01
id125765

fieldvalue
prime_id98188
person_id9
machineDitto P4 P4
whatprime
notesCommand: /home/ditto/client/pfgw -tp -q"266206*5^608649-1" 2>&1
PFGW Version 20031027.x86_Dev (Beta 'caveat utilitor') [FFT v22.13 w/P4]
Primality testing 266206*5^608649-1 [N+1, Brillhart-Lehmer-Selfridge]
Running N+1 test using discriminant 7, base 1+sqrt(7)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(196608,19) to FFT(196608,18)
Reduced from FFT(196608,18) to FFT(196608,17)
Reduced from FFT(196608,17) to FFT(196608,16)
2826532 bit request FFT size=(196608,16)
Running N+1 test using discriminant 7, base 3+sqrt(7)
Using SSE2 FFT
Adjusting authentication level by 1 for PRIMALITY PROOF
Reduced from FFT(196608,19) to FFT(196608,18)
Reduced from FFT(196608,18) to FFT(196608,17)
Reduced from FFT(196608,17) to FFT(196608,16)
2826532 bit request FFT size=(196608,16)
Calling Brillhart-Lehmer-Selfridge with factored part 100.00%
266206*5^608649-1 is prime! (300453.1659s+0.1713s)
[Elapsed time: 3.48 days]
modified2011-03-25 10:27:30
created2011-02-10 15:38:02
id125766

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