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August 18th, 2018, 12:32 PM   #1
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Conjecture concerning a subset of Sofie-Germain primes

Conjecture:

If and only if P(n) and P(n * 2 + 1) are true then n belongs to a subset of Sofie-Germain primes, where P is a boolean function defined as P(m) = { true if 2^((m +1) / 2) = -2 mod m; otherwise false }.

Any idea how to disprove such a thing (or even just a counterexample)?
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August 18th, 2018, 01:24 PM   #2
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Sophie Germain is the name of a person. No hyphen in the name.

https://en.wikipedia.org/wiki/Sophie_Germain

Not like Birch-Swinnerton-Dyer, which is two people!
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August 18th, 2018, 05:24 PM   #3
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Damn! Conjecture is false.

First counterexample: 16070429 = 1637 * 9817
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