Quad-power prime seeds: Difference between revisions

=={{header|Python}}==

<syntaxhighlight lang=python>""" quad-power prime root numbers """

from sympy import isprime

def isquadpowerprime(cand):

""" return if is a quad power prime root number """

return all(isprime(i) for i in

[cand + cand + 1, cand**2 + cand + 1, cand**3 + cand + 1, cand**4 + cand + 1])

qpprimes = [k for k in range(10_100_000) if isquadpowerprime(k)]

for i in range(50):

print(f'{qpprimes[i]: 9,}', end='\n' if (i + 1) % 10 == 0 else '')

for j in range(1_000_000, 10_000_001, 1_000_000):

for p in qpprimes:

if p > j:

print(f'The first quad-power prime seed over {j:,} is {p:,}')

break

</syntaxhighlight>{{out}}

<pre>

1 2 5 6 69 131 426 1,665 2,129 2,696

5,250 7,929 9,689 13,545 14,154 14,286 16,434 19,760 25,739 27,809

29,631 36,821 41,819 46,619 48,321 59,030 60,500 61,955 62,321 73,610

77,685 79,646 80,535 82,655 85,251 86,996 91,014 96,566 97,739 105,939

108,240 108,681 119,754 122,436 123,164 126,489 140,636 150,480 153,179 163,070

The first quad-power prime seed over 1,000,000 is 1,009,286

The first quad-power prime seed over 2,000,000 is 2,015,496

The first quad-power prime seed over 3,000,000 is 3,005,316

The first quad-power prime seed over 4,000,000 is 4,004,726

The first quad-power prime seed over 5,000,000 is 5,023,880

The first quad-power prime seed over 6,000,000 is 6,000,554

The first quad-power prime seed over 7,000,000 is 7,047,129

The first quad-power prime seed over 8,000,000 is 8,005,710

The first quad-power prime seed over 9,000,000 is 9,055,151

The first quad-power prime seed over 10,000,000 is 10,023,600

</pre>