## Powers of Two Primes

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• Powers of Two Numbers are 1 21 421 8421 168421 32168421 6432168421 1286432168421 ... The conjecture is that 421 is the only Power of Two Prime. The other
Message 1 of 2 , Aug 11, 2007
Powers of Two Numbers are

1
21
421
8421
168421
32168421
6432168421
1286432168421
...

The conjecture is that 421 is the only Power of Two Prime.

The other conjecture is that alternate power of two numbers
are divisible by 3.

Milton L. Brown
• ... Proof: Sum(i=0..N, 10^something(i)*2^i) mod 3 = Sum(i=0..N, 2^i) mod 3 = 2^(N+1)-1 mod 3 = 0 for odd N, 1 for even N. Q.E.D. Peter -- [Name] Peter Kosinar
Message 2 of 2 , Aug 11, 2007
> The other conjecture is that alternate power of two numbers
> are divisible by 3.

Proof:
Sum(i=0..N, 10^something(i)*2^i) mod 3 =
Sum(i=0..N, 2^i) mod 3 =
2^(N+1)-1 mod 3 =
0 for odd N, 1 for even N.
Q.E.D.

Peter

--
[Name] Peter Kosinar [Quote] 2B | ~2B = exp(i*PI) [ICQ] 134813278
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