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pseudoprime

Type of Math Object: 
Definition
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Mathematics Subject Classification

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I'm posing the conjecture:
Does this criteria always expose 2-pseudoprimes ???
(sorry if I'm not using the maths totally correctly)

let 2^(Q-1) mod Q == 1 where Q = 4m +1 (possibly pseudo)
now, 'Q' is prime iff the above criteria and...
2^(Q-1)-2 mod 'q' == -1, 0
where 'q' is 'Q' w/all 2's factored out.

it approves primes...
eg. Q= 641 = 4*160 +1 and 2^640 mod 641 == 1
q= 5 or 640 w/all the 2's factored out
then, 2^640-2 mod 5 == -1, so 641 truly is prime.

and dis-allows pseudos...
eg. Q= 341 = 4*85 +1 and 2^340 mod 341 == 1
q= 85 or 340 w/all 2's factored out
then, 2^340-2 mod 85 == 14, so 341 is pseudo.

eg. Q= 101 = 4*25 +1 and 2^100 mod 101 == 1
q= 25 or 100 w/all the 2's factored out
then, 2^100-2 mod 25 == -1, so 101 truly is prime.

I think that it's always 'true', but can't prove it!

from a cursory glance, it looks O.K.?
it takes a pseudo to know a pseudo...

Bill Bouris

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