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## Re: [PrimeNumbers] PSPs and squarefreeness

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• 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 primes sols
Message 1 of 4 , Apr 25 6:06 PM
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
primes

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

etc

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
coprime bases

Jason

> 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?
>
> Phil
>
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