Thanks a lot this helps, I was wondering if looking for the next prime from a random value is introducing some bias compared to building iterating on random numbers until one fall on a prime, (which is obviously more time consuming).
Also I am curious though about your comment: how does the NSA or ESA get to know the secret,
do they bruteforce "weak" primes ?

In reply to Re^2: How to get good primes for DH agreement ? by iglake
in thread How to get good primes for DH agreement ? by iglake

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