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## RE: we are now 1087...

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• Can t think of anything off the top of my head, and David Wells s Curious and Interesting Numbers does not have an entry. According to Chris Caldwell s Prime
Message 1 of 3 , Jul 13 2:25 PM
Can't think of anything off the top of my head, and David
Wells's "Curious and Interesting Numbers" does not have an entry.
According to Chris Caldwell's Prime Curios

1087 is a prime factor of the 32nd Lucas number (the first such
number with index of form 2^n that is composite).
The largest known number such that (10000^n+1)/10001 is probably
prime.

Perhaps we should try and find another half a dozen new members, then
we are 1093. Wells's entry for 1093 is a bit more interesting:

"2^1092 - 1 is divisible by 1093. Only one other number is known
below 4 * 10^12 with this property, 3511.
In 1909 Wieferich created a sensation by proving that if Fermat's
equation, x^p + y^p = z^p, has a solution in whih p is an odd prime
that does notr divide any of x, y or z, then 2^(p-1) - 1 is divisible
by p^2. As facts about Fermat's last theorem go, this is remarkably
simple. That 1093 and 3511 are the only solutions below 4 * 10^12
means that only these two cases of Fermat's theorem need to be
considered, below that limit, of p does not divide xyz."

Douglas Chester

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