Re: [PrimeNumbers] PSPs and squarefreeness
On Thursday 25 April 2002 22:42, you wrote:
To anwser the other questions
The New book of prime number records , has a section on these Wiefierich
sols to a^(p-1)=1 mod p^2
a=2 p=1093,3511 no others known for p<4*10e12
a=3 p=11,1006003 p<2^32
a=5 p=20771,40487,53471161,1645333507 p<2^32
1093^2,3511^2,29*113*1093^2 are base 2 strong pseudoprimes
NOTE at least two of these should be in your table , your table probably is
for square free base 2 strong pseudoprimes only.
I'm fairly certain that base b strong pseudoprimes have similar analogs
Although as the Wiefierich primes are very rare there are very few(NONE ?)
numbers which are not square free and are strong pseudoprimes to multiple
> Can 2-SPRPs have repeated factors?
> I thought I'd just thrown together a proof of such, but it had a
> gaping flaw (it wouldn't even have proved _carmichaels_ have that
> property, it was so broken), so I reckoned it was best to just ask
> the experts. I couldn't find any in my files (the standard 10^13
> table seemed devoid of them). In other bases, 9, 25, 49, 121, 169
> etc. can be pseudo-prime, so if it were to be true for 2-SPRPs, would
> 2 be the only base which had the property?
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