# 32120580 - 3623816 - 1

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Description: 32120580 - 3623816 - 1 PRP [none] This prime has 1 user comment below. CH9 : Zhou, OpenPFGW, CHG 1011774   (log10 is 1011773.7903334) 872 (digit rank is 1) 414 short 5/12/2019 08:20:20 CDT 5/13/2019 12:50:22 CDT 126454 Verify, TrialDiv 46.6689 (normalized score 9.1354)

Lei Zhou writes (12 May 2019):  (report abuse)
 This is a balanced ternary prime with 3 non-zero digits (in balanced ternary base). p+1=3^2120580-3^623816=Phi(1,3)*Phi(2,3)*Phi(4,3)*Phi(383,3)*Phi(766,3)*Phi(977,3)*Phi(1532,3)*Phi(1954,3)*Phi(3908,3)*Phi(374191,3)*Phi(748382,3)*Phi(1496764,3) which was found with a list of small factors in the proof pack here. Using the above small factors as help, OpenPFGW provides that it is a Fermat and Lucas PRP: \$ ./pfgw -tc -k -h"cp_2120580_-3_623816_-1.helper" cp_2120580_-3_623816_-1 Primality testing 3^2120580-3^623816-1 [N-1/N+1, Brillhart-Lehmer-Selfridge] Reading factors from helper file cp_2120580_-3_623816_-1.helper Running N-1 test using base 41 Running N+1 test using discriminant 47, base 1+sqrt(47) 3^2120580-3^623816-1 is Fermat and Lucas PRP! (141118.4747s+0.0156s) Using F = 2 and G = the product of the above listed small factors, CHG pari script proved that this is a prime number. (full CHG output is too long to be posted here. Verification is the following) The result is certified by David Broadhurst's verifier chgcertd.gp. Testing a PRP called "cp_2120580_-3_623816_-1.in". Pol[1, 1] with [h, u]=[4, 1] has ratio=2.796269296969836082 E-179332 at X, ratio=1.9778997813013111843 E-125427 at Y, witness=2. Pol[2, 1] with [h, u]=[6, 2] has ratio=2.4698351139240039616 E-53343 at X, ratio=3.450462696097655256 E-63276 at Y, witness=2. Validated in 8 sec. The certificate is available at here.

#### 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_id126454
person_id9
machineUsing: Xeon 4c+4c 3.5GHz
whatprp
notesCommand: /home/caldwell/client/pfgw/pfgw64 -tp -q"3^2120580-3^623816-1" 2>&1 PFGW Version 3.7.7.64BIT.20130722.x86_Dev [GWNUM 27.11] Primality testing 3^2120580-3^623816-1 [N+1, Brillhart-Lehmer-Selfridge] Running N+1 test using discriminant 41, base 1+sqrt(41) Calling Brillhart-Lehmer-Selfridge with factored part 29.42% 3^2120580-3^623816-1 is Lucas PRP! (101371.4113s+0.0429s) [Elapsed time: 28.16 hours]
modified2020-07-07 17:30:13
created2019-05-12 08:21:01
id172139

Query times: 0.0006 seconds to select prime, 0.0008 seconds to seek comments.