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

>

> __________________________________________________

> Do You Yahoo!?

> Yahoo! Games - play chess, backgammon, pool and more

> http://games.yahoo.com/

>

>

> Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com

> The Prime Pages : http://www.primepages.org

>

>

>

> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/