Fermat numbers: Difference between revisions
Add PARI/GP implementation
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Pollard rho try factor 350001591824186871106763863899530746217943677302816436473017740242946077356624684213115564488348300185108877411543625345263121839042445381828217455916005721464151569276047005167043946981206545317048033534893189043572263100806868980998952610596646556521480658280419327021257968923645235918768446677220584153297488306270426504473941414890547838382804073832577020334339845312084285496895699728389585187497914849919557000902623608963141559444997044721763816786117073787751589515083702681348245404913906488680729999788351730419178916889637812821243344085799435845038164784900107242721493170135785069061880328434342030106354742821995535937481028077744396075726164309052460585559946407282864168038994640934638329525854255227752926198464207255983432778402344965903148839661825873175277621985527846249416909718758069997783882773355041329208102046913755441975327368023946523920699020098723785533557579080342841062805878477869513695185309048285123705067072486920463781103076554014502567884803571416673251784936825115787932810954867447447568320403976197134736485611912650805539603318790667901618038578533362100071745480995207732506742832634459994375828162163700807237997808869771569154136465922798310222055287047244647419069003284481 elapsed time = 114 ms (factor = 63766529).
F₁₂ = 114689 * 26017793 * 63766529 * (C1213)</pre>
=={{header|PARI/GP}}==
{{trans|Julia}}
<syntaxhighlight lang="PARI/GP">
\\ Define a function to calculate Fermat numbers
fermat(n) = 2^(2^n) + 1;
\\ Define a function to factor Fermat numbers up to a given maximum
\\ and optionally just print them without factoring
factorfermats(mymax, nofactor=0) =
{
local(fm, factors, n);
for (n = 0, mymax,
fm = fermat(n);
if (nofactor,
print("Fermat number F(", n, ") is ", fm, ".");
next;
);
factors = factorint(fm);
if (matsize(factors)[1] == 1 && factors[1,2] == 1, \\ Check if it has only one factor with exponent 1 (i.e., prime)
print("Fermat number F(", n, "), ", fm, ", is prime.");
,
print("Fermat number F(", n, "), ", fm, ", factors to ", (factors), ".");
);
);
}
{
\\ Example usage
factorfermats(9, 1); \\ Print Fermat numbers without factoring
print(""); \\ Just to add a visual separator in the output
factorfermats(10); \\ Factor Fermat numbers
}
</syntaxhighlight>
{{out}}
<pre>
Fermat number F(0) is 3.
Fermat number F(1) is 5.
Fermat number F(2) is 17.
Fermat number F(3) is 257.
Fermat number F(4) is 65537.
Fermat number F(5) is 4294967297.
Fermat number F(6) is 18446744073709551617.
Fermat number F(7) is 340282366920938463463374607431768211457.
Fermat number F(8) is 115792089237316195423570985008687907853269984665640564039457584007913129639937.
Fermat number F(9) is 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084097.
Fermat number F(0), 3, is prime.
Fermat number F(1), 5, is prime.
Fermat number F(2), 17, is prime.
Fermat number F(3), 257, is prime.
Fermat number F(4), 65537, is prime.
Fermat number F(5), 4294967297, factors to [641, 1; 6700417, 1].
Fermat number F(6), 18446744073709551617, factors to [274177, 1; 67280421310721, 1].
Fermat number F(7), 340282366920938463463374607431768211457, factors to [59649589127497217, 1; 5704689200685129054721, 1].
Fermat number F(8), 115792089237316195423570985008687907853269984665640564039457584007913129639937, factors to [1238926361552897, 1; 93461639715357977769163558199606896584051237541638188580280321, 1].
</pre>
=={{header|Perl}}==
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