mersenneforum.org Sufficient but not necessary condition for primality?
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2023-05-06, 23:50   #23
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

53·19 Posts

The problem with Wilson’s theorem is that, while being deterministic, it also works for all primes and not a subset of them like the Sweety’s concept. As such it does not concur with the OP.
Quote:
 No soup for you, NEXT.

Last fiddled with by a1call on 2023-05-07 at 00:09

 2023-05-18, 03:12 #24 rudy235     Jun 2015 Vallejo, CA/. 116110 Posts Although this is probably already known (by analogy) you can say that for n to be prime, a sufficient but not necessary condition is that An-1/(A-1) is prime. Of course A can be any positive integer>1 _ as long it is not of the form jk where k ≥ 2_ we have For A=2 .A000043 Mersenne Primes For A=3 .A028491 For A=5 .A004061 For A=6 .A004062 For A=7 .A004063 For A=10 A004023 Repunits For A=12 A004064 E&OE
2023-05-18, 10:49   #25
slandrum

Jan 2021
California

22·137 Posts

Quote:
 Originally Posted by rudy235 An-1/(10-1) is prime.
Shouldn't that be (An-1)/(A-1)

Last fiddled with by slandrum on 2023-05-18 at 10:50

 2023-05-18, 12:11 #26 Andrew Usher   Dec 2022 3·5·29 Posts Yes, I'm assuming that as the only sensible meaning. That (A^n - 1)/(A - 1) is prime is certainly a sufficient condition (A, n integers > 1). Now does it become necessary when generalised? That is, is there always for n prime some base A that yields a prime? Well-founded conjecture says there are, and infinitely many of them.
2023-05-18, 18:59   #27
rudy235

Jun 2015
Vallejo, CA/.

33×43 Posts

[C]
Quote:
 Originally Posted by slandrum Shouldn't that be (An-1)/(A-1)
Yeah! Sorry, when I edited the post, I changed the part that had ‘10’ to A but then left a ‘10’ without changing it.

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