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drummerslowrise

Message boards :
Wieferich and WallSunSun Prime Search :
We found a nearWieferich with A ≤ 10
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Dear all,
User tng and double checker Grzegorz Roman Granowski just found the following: 3156824277937156367 is a Wieferich special instance (+1 +7 p) (about 3*10^18).
This A=+7 is the lowest A seen since p=2276306935816523 (about 2*10^15, in the year 2006). There is a list of nearWieferichs with A at most 10 on Wikipedia, NearWieferich primes, and there is a list of nearWieferichs with A strictly below 10 [in the LINKS section] on OEIS A246568.
Congratulations to tng!
An overview of new WW finds is on WW Statistics.
/JeppeSN  


Congrats to tng and Grzegorz Roman Granowski !
____________
"Accidit in puncto, quod non contingit in anno."
Something that does not occur in a year may, perchance, happen in a moment.  

Ravi FernandoProject administrator Volunteer tester Project scientist Send message
Joined: 21 Mar 19 Posts: 210 ID: 1108183 Credit: 13,073,385 RAC: 6,263

This A=+7 is the lowest A seen since p=2276306935816523 (about 2*10^15, in the year 2006).
In particular, the ratio A/p ~ 2.22 * 10^18 is easily the lowest yet for a nearWieferich, excluding the two known Wieferich primes of course. The previous record for this was 40/1713380095653669769 ~ 1.27 * 10^17, found by none other than Grzegorz Roman Granowski early last month.  


This A=+7 is the lowest A seen since p=2276306935816523 (about 2*10^15, in the year 2006).
In particular, the ratio A/p ~ 2.22 * 10^18 is easily the lowest yet for a nearWieferich, excluding the two known Wieferich primes of course. The previous record for this was 40/1713380095653669769 ~ 1.27 * 10^17, found by none other than Grzegorz Roman Granowski early last month.
Yes, maybe you could make a Wieferich version of my nearWallSunSun sequence OEIS A339855. In one possible version of it, it would end at the first Wieferich prime:3, 5, 7, 17, 31, 59, 71, 251, 379, 1093.
But you could also make a version that started from 3 but ignored true Wieferich primes:3, 5, 7, 17, 31, 59, 71, 251, 379, 1733, 2633, 2659, 15823, 60631, 352691, ...
Or you could make a version that started from just after the second Wieferich prime 3511 and ended at the third Wieferich prime (if it exists):3517, 3527, 3541, 3923, 4723, 5179, 9419, 13463, 15329, 15823, 60631, 352691, ...
In fact, you could probably submit all these three if you wanted. Do any of you have any opinion on that?
There is another question with these nearWieferichs, because there are two conventions on how to measure nearness. PrimeGrid (like some of its predecessors) looks at 2^{(p1)/2} modulo p^2, and defines A based on that. But it is maybe more natural to include the final squaring and instead consider 2^{p1} modulo p^2, and if you read the Wikipedia section I linked, this was done by Dorais & Klyve, and gives another list of nearWieferichs.
/JeppeSN  


Congrats tng!  


Congrats to tng and Grzegorz Roman Granowski !
Thank You ...
my ... power of gpu is going to be updated soon ... and hopefully ...
we'll find a = 0 ... SOON ...
best regards, Grzegorz Roman Granowski
____________
 


Or you could make a version that started from just after the second Wieferich prime 3511 and ended at the third Wieferich prime (if it exists):3517, 3527, 3541, 3923, 4723, 5179, 9419, 13463, 15329, 15823, 60631, 352691, ...
In fact, you could probably submit all these three if you wanted. Do any of you have any opinion on that?
I like this one the most. Ignoring the two initial Wieferich primes seems like a reasonable thing to do, given how close they are to zero. From here, I think that the interesting property is the gap between subsequent terms.
A fourth option though would be to include all terms and "reset" at each Wieferich prime.3, 5, 7, 17, 31, 59, 71, 251, 379, 1093, *terms between 1093 and 3511*, 3511, 3517, 3527, 3541, 3923, 4723, 5179...
Not sure if OEIS accepts resetting sequences at specific terms though.
Congrats to tng and Grzegorz Roman Granowski for the excellent find!  

Message boards :
Wieferich and WallSunSun Prime Search :
We found a nearWieferich with A ≤ 10 