A Curious Sequence of Prime Numbers

Re:A Curious Sequence of Prime Numbers by saagarjha on Sunday May 26, 2019 @07:24PM (#20018246)

2^32+1 is likely reaching the limits of what an elementary school child is able to do by hand. As for the larger numbers: they do get unwieldy quickly, but I think it might be possible to manually find the factors of them with probabilistic primality testing.

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Re:A Curious Sequence of Prime Numbers by lifthrasiir on Sunday May 26, 2019 @10:46PM (#20019059)

Well, the child will be bored much earlier :-)

For Fermat numbers 2^(2^n) + 1, it is well known that every prime factor should have the form k 2^(n+2) + 1. The sequence (A007117) thus goes like: k = 5 for n = 5 (Euler in 1732, very managable), k = 1071 for n = 6 (Thomas Clausen in 1854) and k = 116503103764643 for n = 7 (only known in 1970 after the modern computer).

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