Script doesn't seem to be execute properly
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Manuel Barros on 7 Dec 2018
Commented: Manuel Barros on 10 Dec 2018
I was hoping to acquire some help on how to make my program work efficiently and not take a substantial amount of time to finish:
count=count + 1;
This program outputs a number p greater than a such that p is prime and (p-1)/2 is prime. However I've noticed that for any number a greater than approximately 15 digits, the program will take an absurd amount of time to finish, which isn't ideal since I need to test numbers of the order 10^50.
Walter Roberson on 7 Dec 2018
Beyond about 4E15 the distance between adjacent representable doubles becomes greater than 1. p becomes forced to be even (and so not a prime) and p-1 becomes the same as p .
You can do marginally better by switching to uint64, which gets you to about 1.8E19 . But you cannot get beyond that using ordinary numeric forms.
You need to switch to a variable precision toolbox, such as Symbolic Toolbox, or John D'Errico's File Exchange contribution for variable precision integers.
Walter Roberson on 8 Dec 2018
Then it is going to depend upon the quality of implementation of isprime() or nextprime() . There is a possibility that it might be faster to test
test_vals = p : 2 : p + 10000;
candidate_mask = isprime(test_vals);
next_few_primes = test_vals(candidate_mask);
instead of looping doing nextprime().
But that is going to depend on how the isprime() and nextprime() are implemented in the symbolic package.
More Answers (1)
Christopher Creutzig on 10 Dec 2018
Edited: Christopher Creutzig on 10 Dec 2018
In your code, you spend a lot of time computing the same prime over and over again. Do not start the search at a+1 for the second search, but start after the prime you already found.
It might also be marginally faster to look for the next prime q starting at a/2 such that p=2*q+1 is also prime.
>> a = sym('12345678901234567890');
>> q = nextprime(fix(a/2));
>> while ~isprime(2*q+1), q = nextprime(q+1); end
Elapsed time is 4.304840 seconds.
>> [q, 2*q+1]
[ 6172839450617290091, 12345678901234580183]
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