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From: Turing's Worst Nightmare on 16 May 2010 02:02
2p+1/3 is prime ==> 25^2p-1 = 25 (mod 2p + 1)

Np is a 5-PRP =) 252p-1 ยด 25 (mod 2p + 1) =) Np is a 125-PRP

S (125-PRP) < or = S (fast test) < or = S (5-PRP)

Remark: It exists a generalization of the test for numbers of the
form:

6p+1/17 ,
256p+1/257 and
65536p+1/65537 . (Cf. [3])
From: Turing's Worst Nightmare on 16 May 2010 02:02
2p+1/3 is prime ==> 25^2p-1 == 25 (mod 2^p + 1)

Np is a 5-PRP ==> 252^2^p-1 == 25 (mod 2^p + 1) => Np is a 125-PRP

S (125-PRP) < or = S (fast test) < or = S (5-PRP)

Remark: It exists a generalization of the test for numbers of the
form:

6p+1/17 ,
256p+1/257 and
65536p+1/65537 . (Cf. [3])
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