Anonymous user
Semiprime: Difference between revisions
PARI and GP
(→{{Header|Go}}: simplification) |
(PARI and GP) |
||
Line 129:
Description: factor the number and count the primes in the factorization, is it 2?
=={{header|PARI/GP}}==
<lang parigp>issemi(n)=bigomega(n)==2</lang>
A faster version might use trial division and primality testing:
<lang parigp>issemi(n)={
forprime(p=2,97,if(n%p==0, return(isprime(n/p))));
if(isprime(n), return(0));
bigomega(n)==2
};</lang>
To get faster, partial factorization can be used. At this time GP does not have access to meaningful partial factorization (though it can get it to some extent through flags on <code>factorint</code>), so this version is in PARI:
<lang c>long
issemiprime(GEN n)
{
if (typ(n) != t_INT)
pari_err_TYPE("issemiprime", n);
if (signe(n) <= 0)
return 0;
ulong nn = itou_or_0(n);
if (nn)
return uissemiprime(nn);
pari_sp ltop = avma;
if (!mpodd(n)) {
long ret = mod4(n) && isprime(shifti(n, -1));
avma = ltop;
return ret;
}
long p;
forprime_t primepointer;
u_forprime_init(&primepointer, 3, 997);
while ((p = u_forprime_next(&primepointer))) {
if (dvdis(n, p)) {
long ret = isprime(diviuexact(n, p));
avma = ltop;
return ret;
}
}
if (isprime(n))
return 0;
if (DEBUGLEVEL > 3)
pari_printf("issemi: Number is a composite with no small prime factors; using general factoring mechanisms.");
GEN fac = Z_factor_until(n, shifti(n, -1)); /* Find a nontrivial factor -- returns just the factored part */
GEN expo = gel(fac, 2);
GEN pr = gel(fac, 1);
long len = glength(expo);
if (len > 2) {
avma = ltop;
return 0;
}
if (len == 2) {
if (cmpis(gel(expo, 1), 1) > 0 || cmpis(gel(expo, 2), 1) > 0) {
avma = ltop;
return 0;
}
GEN P = gel(pr, 1);
GEN Q = gel(pr, 2);
long ret = isprime(P) && isprime(Q) && equalii(mulii(P, Q), n);
avma = ltop;
return ret;
}
if (len == 1) {
long e = itos(gel(expo, 1));
if (e == 2) {
GEN P = gel(pr, 1);
long ret = isprime(P) && equalii(sqri(P), n);
avma = ltop;
return ret;
} else if (e > 2) {
avma = ltop;
return 0;
}
GEN P = gel(pr, 1);
long ret = isprime(P) && isprime(diviiexact(n, P));
avma = ltop;
return ret;
}
pari_err_BUG(pari_sprintf("Z_factor_until returned an unexpected value %Ps at n = %Ps, exiting...", fac, n));
avma = ltop;
return 0; /* never used */
}</lang>
=={{header|Perl 6}}==
| |||