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:
|Description:||742478255901 · 240069 + 1|
|Verification status (*):||Proven|
|Official Comment:||Cunningham chain 2nd kind (4p-3)|
|Proof-code(s): (*):||p395 : Angel, Augustin, NewPGen, OpenPFGW|
|Decimal Digits:||12074 (log10 is 12073.84158)|
|Rank (*):||71693 (digit rank is 1)|
|Entrance Rank (*):||69661|
|Currently on list? (*):||short|
|Submitted:||9/9/2016 10:13:17 CDT|
|Last modified:||9/9/2016 20:50:31 CDT|
|Score (*):||33.024 (normalized score 0)|
There are certain forms classed as
archivable: these prime may (at times)
remain on this list even if they do not make
the Top 5000 proper. Such primes are tracked with archival
- Cunningham Chains (2nd kind) (archivable class *)
- Prime on list: yes, rank 1, weight 42.2067079551582
Subcategory: "Cunningham chain 2nd kind (4p-3)"
(archival tag id 218419, tag last modified 2016-09-09 20:50:34)
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.
|machine||Using: Xeon 4c+4c 3.5GHz|
|notes||Command: /home/caldwell/client/pfgw/pfgw64 -t -q"742478255901*2^40069+1" 2>&1|
PFGW Version 126.96.36.199BIT.20130722.x86_Dev [GWNUM 27.11]
Primality testing 742478255901*2^40069+1 [N-1, Brillhart-Lehmer-Selfridge]
Running N-1 test using base 5
Calling Brillhart-Lehmer-Selfridge with factored part 99.90%
742478255901*2^40069+1 is prime! (0.8238s+0.0002s)
[Elapsed time: 1.00 seconds]
Query times: 0.0005 seconds to select prime, 0.0005 seconds to seek comments.