login
(F5,F7,F8,F9,F10,F11,F12,F14) - 10^n = prime where F stands for the Fermat numbers 2^2^x + 1 where x corresponds to 5,7,8,9,10,11,12 and 14.
0

%I #1 Feb 24 2006 03:00:00

%S 2,16,28,6,30,72,130,255

%N (F5,F7,F8,F9,F10,F11,F12,F14) - 10^n = prime where F stands for the Fermat numbers 2^2^x + 1 where x corresponds to 5,7,8,9,10,11,12 and 14.

%C This sequence shows that the difference between a composite number and a prime rests on the modification of a single decimal digit. Note that F6 and F13 regarding the Fermat numbers are exceptions to this rule.

%e F5 - 10^2 = 4294967197 = prime

%t Position[PrimeQ[Table[2^2^5 + 1 - 10^n, {n, 10}]], True]

%K nonn

%O 2,1

%A Joao Carlos Leandro da Silva (zxawyh66(AT)yahoo.com), Jan 30 2006