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MillerRabinPrime.m
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MillerRabinPrime.m
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function isp = MillerRabinPrime(n)
% Rabin, Michael O. (1980), "Probabilistic algorithm for testing primality",
% Journal of Number Theory, 12 (1): 128–138
isp = true;
n = n(:);
if n <= 4
isp = n == 2 || n == 3;
return;
elseif mod(n, 2) == 0
isp = false;
return;
end
% extract powers of 2
n = uint64(n);
d = n - 1;
while ~bitand(d, 1)
d = d / 2;
end
% deterministic bases for Miller-Rabin up to 2^64
% Sinclair, J. (n.d.). Deterministic variants of the Miller-Rabin
% primality test.
% Miller-Rabin SPRP bases records. https://miller-rabin.appspot.com/.
if n >= 3071837692357849
numsToTry = [2, 325, 9375, 28178, 450775, 9780504, 1795265022];
elseif n < 1373653
numsToTry = [2, 3];
elseif n < 4759123141
numsToTry = [2, 7, 61];
elseif n < 47636622961201
numsToTry = [2, 2570940, 211991001, 3749873356];
else
numsToTry = [2, 75088, 642735, 203659041, 3613982119];
end
for numToTry = uint64(numsToTry)
if ~millerRabinTest(numToTry, d, n)
isp = false;
return;
end
end
end
function isp = millerRabinTest(base, exp, n)
% base^exp % n
r = ModExp(base, exp, n);
isp = false;
if r == 1 || r == n - 1
isp = true;
return;
end
while exp ~= n - 1
r = ModExp(r, 2, n);
exp = exp + exp;
if r == n - 1
isp = true;
return;
end
end
end