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lucas primality test small primes
Clash Royale CLAN TAG#URR8PPP
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I'm writing a a Lucas primality test using the Selfridge parameters, but it seems to indicate that 5 and 11 are not prime. For both of those, the Jacobi number is 0.
In the case of 5, the first Jacobi test you try is (5/5) = 0, so you stop and return composite.
In the case of 11, you do (5/11) = 1, (-7/11) = 1, (9/11) = 1, (-11/11) = 0.
I found no other examples so far where my test returns it's composite while it's prime.
They both stop when |D| = n. I can't find any indication that I should stop searching for D when D reaches some value, only that I should check that it's not a perfect square.
Is |D| = n some special case? Should I continue searching for D in that case? At least 5 and 11 will find -1 for the Jacobi symbol for the next value in the sequence.
primality-test
asked Jul 30 at 4:44
Kurt Roeckx
1
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up vote
-1
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I'm writing a a Lucas primality test using the Selfridge parameters, but it seems to indicate that 5 and 11 are not prime. For both of those, the Jacobi number is 0.
In the case of 5, the first Jacobi test you try is (5/5) = 0, so you stop and return composite.
In the case of 11, you do (5/11) = 1, (-7/11) = 1, (9/11) = 1, (-11/11) = 0.
I found no other examples so far where my test returns it's composite while it's prime.
They both stop when |D| = n. I can't find any indication that I should stop searching for D when D reaches some value, only that I should check that it's not a perfect square.
Is |D| = n some special case? Should I continue searching for D in that case? At least 5 and 11 will find -1 for the Jacobi symbol for the next value in the sequence.
primality-test
asked Jul 30 at 4:44
Kurt Roeckx
1
I added a "if (j != 1 && |D| != n) break" in my loop, meaning we want to stop searching if the Jacobi result is 0 or -1, but skip the case where the Jacobi test is not meaningful. Optionally I could skip the Jacobi test entirely but that's a dubious micro-optimization. Realistically this only happens for 5 and 11.
– DanaJ
2 days ago
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I'm writing a a Lucas primality test using the Selfridge parameters, but it seems to indicate that 5 and 11 are not prime. For both of those, the Jacobi number is 0.
In the case of 5, the first Jacobi test you try is (5/5) = 0, so you stop and return composite.
In the case of 11, you do (5/11) = 1, (-7/11) = 1, (9/11) = 1, (-11/11) = 0.
I found no other examples so far where my test returns it's composite while it's prime.
They both stop when |D| = n. I can't find any indication that I should stop searching for D when D reaches some value, only that I should check that it's not a perfect square.
Is |D| = n some special case? Should I continue searching for D in that case? At least 5 and 11 will find -1 for the Jacobi symbol for the next value in the sequence.
primality-test
asked Jul 30 at 4:44
Kurt Roeckx
1
I'm writing a a Lucas primality test using the Selfridge parameters, but it seems to indicate that 5 and 11 are not prime. For both of those, the Jacobi number is 0.
In the case of 5, the first Jacobi test you try is (5/5) = 0, so you stop and return composite.
In the case of 11, you do (5/11) = 1, (-7/11) = 1, (9/11) = 1, (-11/11) = 0.
I found no other examples so far where my test returns it's composite while it's prime.
They both stop when |D| = n. I can't find any indication that I should stop searching for D when D reaches some value, only that I should check that it's not a perfect square.
Is |D| = n some special case? Should I continue searching for D in that case? At least 5 and 11 will find -1 for the Jacobi symbol for the next value in the sequence.
primality-test
asked Jul 30 at 4:44
Kurt Roeckx
1
asked Jul 30 at 4:44
Kurt Roeckx
1
asked Jul 30 at 4:44
Kurt Roeckx
1
asked Jul 30 at 4:44
Kurt Roeckx
1
1
I added a "if (j != 1 && |D| != n) break" in my loop, meaning we want to stop searching if the Jacobi result is 0 or -1, but skip the case where the Jacobi test is not meaningful. Optionally I could skip the Jacobi test entirely but that's a dubious micro-optimization. Realistically this only happens for 5 and 11.
– DanaJ
2 days ago
add a comment |Â
I added a "if (j != 1 && |D| != n) break" in my loop, meaning we want to stop searching if the Jacobi result is 0 or -1, but skip the case where the Jacobi test is not meaningful. Optionally I could skip the Jacobi test entirely but that's a dubious micro-optimization. Realistically this only happens for 5 and 11.
– DanaJ
2 days ago
I added a "if (j != 1 && |D| != n) break" in my loop, meaning we want to stop searching if the Jacobi result is 0 or -1, but skip the case where the Jacobi test is not meaningful. Optionally I could skip the Jacobi test entirely but that's a dubious micro-optimization. Realistically this only happens for 5 and 11.
– DanaJ
2 days ago
I added a "if (j != 1 && |D| != n) break" in my loop, meaning we want to stop searching if the Jacobi result is 0 or -1, but skip the case where the Jacobi test is not meaningful. Optionally I could skip the Jacobi test entirely but that's a dubious micro-optimization. Realistically this only happens for 5 and 11.
– DanaJ
2 days ago
add a comment |Â
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I added a "if (j != 1 && |D| != n) break" in my loop, meaning we want to stop searching if the Jacobi result is 0 or -1, but skip the case where the Jacobi test is not meaningful. Optionally I could skip the Jacobi test entirely but that's a dubious micro-optimization. Realistically this only happens for 5 and 11.
– DanaJ
2 days ago