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A prime GCD adventure (Posted on 2024-05-03) Difficulty: 3 of 5
Determine the greatest common divisor of the numbers p6-7p2+6 where p runs through the prime numbers p≥11.

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 5.0000 (1 votes)

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Some Thoughts calculating a few | Comment 2 of 6 |
For 11 by itself, the GCD of f(11) is just f(11) itself, which is 1770720.

For the series f(11), f(13), ... for larger primes, the GCD appears to be 672.

----
def f(p):
    return  p**6 - 7*p**2 + 6

primes = [p for p in range(11,10000) if isprime(p)]
f_of_p = [f(p) for p in primes]

for i,v in enumerate (primes):
    if gcdList(f_of_p[:(i+1)]) != 672:
        print(v, f_of_p[:(i+1)], gcdList(f_of_p[:(i+1)]))

Output, the only line that prints out is:
11 [1770720] 1770720


  Posted by Larry on 2024-05-03 10:58:16
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