Is (10^y - 1) x (10^y) + 1 prime for any value of y besides 2, 4, 6, and 8?
Don Reble
djr at nk.ca
Mon Nov 29 17:37:20 CET 2004
> ... an obvious reason why (10^y - 1) x (10^y) + 1
> could only produce primes when y is 2, 4, 6, or 8?
Let f(y) = (10^y - 1) * 10^y + 1. One can prove:
If y is odd but not a multiple of 9,
then f(y) is divisible by 7 or 19;
If y is even but not a multiple of 6,
let y=2^k*x (odd x, maximum k);
then f(2^k) divides f(y).
So if f(y) is prime, then
y is a power of two, or y == 0,6,9,12 mod 18.
--
Don Reble djr at nk.ca
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