[Cryptography] Factoring safe semiprimes

[Christian Huitema]

On 10/17/2025 1:16 PM, Pierre Abbat wrote:
> On Friday, October 17, 2025 10:56:25 AM EDT Ron Garret wrote:
>> But I'm still scratching my head trying to figure out what a "Fouvry prime"
>> is.
> A Fouvry prime is a prime p such that p-1 has a prime divisor greater than
> p^(2/3). See https://oeis.org/A073024 .


Is the factor 2/3 arbitrary, or is it the result of some equation?

I had the same concern when considered "semiprimes that aren't close to 
being squares". "Close" is an awfully loose term. That could mean, for 
example, that one of the divisors should be greater than p^x, for some x 
larger than 1/2. But how much larger? If that divider is p/3 and p is 
big enough, it is certainly larger than p^(2/3). Does p meet the "safe 
prime" requirement?

-- Christian Huitema