RFC: nextprime(::BigInt)

[mschauer]

On StackExchange someone asked for a wrapper of the GMP next_prime routine. If there is interest, here is a pull request for a new function nextprime. But compared with the naive

nextprime2(y) = let x = y+1; while(!isprime(x)) x += 1; end; x; end

I get

x = big(1931)*prod(big(primes(1,1933)))÷7230 - 30244 #location of a big prime gap of size 66520
julia> @time nextprime2(x) - x
 33.357414 seconds (199.57 k allocations: 25.378 MB, 0.02% gc time)
66520

julia> @time nextprime(x) - x
 49.900821 seconds (11 allocations: 3.398 KB)
66520

Am I missing something or is __gmpz_nextprime worse than __gmpz_probab_prime_p (both use 25 reps standard)?

@pabloferz

[tkelman]

If we're going to define this, there should be definitions for more than just BigInts.

[pabloferz]

@mschauer AFAIK mpz_nextprime can be slow (though this comparison shows it can be really bad). I agree with Tony in that there should be definitions for other types.

Nonetheless it has been pointed out before that this kind of functions probably belong to a package (to which I agree).

[pabloferz]

Actually the 'naive' loop is probably near to the best you can do, what you would actually need is a faster primality test (BPSW, ECPP or APR). For the loop version you can get rid of the allocations with

function nextprime2(y::BigInt)
    c = BigInt(1)
    x = y + c
    while(!isprime(x))
        ccall((:__gmpz_add,:libgmp), Void, (Ptr{BigInt}, Ptr{BigInt}, Ptr{BigInt}), &x, &x, &c)
    end
    x
end

[mschauer]

Actually the 'naive' loop is probably near to the best you can do

Looks like it is: http://stackoverflow.com/questions/4475996/given-prime-number-n-compute-the-next-prime
Nice insofar that then there is also a natural way to make @tkelman happy and define nextprime for other types in the same way.

[pabloferz]

Given that it seems hard to do much better than this, what we really should focus on is in improving isprime istead, as discussed here #11594.

[mschauer]

#16357