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Old 2018-12-14, 21:27   #6
sweety439's Avatar
Nov 2016

24·157 Posts

For k's make a full covering set with partial algebraic factors, we only take the n for algebraic factors (i.e. not take the n for covering set for fixed prime factors)

e.g. for R24 k=4, we need an even n such that 2*24^(n/2)-1 and 2*24^(n/2)+1 are both primes. (since for odd n, 4*24^n-1 is always divisible by 5, and for even n, 4*24^n-1 = (2*24^(n/2)-1) * (2*24^(n/2)+1), thus we need n such that both these two formulas take prime values)

e.g. for R24 k=6, we need an odd n such that 2^(3q-1)*3^q - 1 and m*2^(3q-1)*3^q + 1 are both primes (where q = (n+1)/2).

e.g. for R19 k=4, we need an even n such that 2*19^(n/2)-1 and (2*19^(n/2)+1)/3 are both primes.
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