The prime generator

The 6th problem in IMO 1987 reads like this:

Given a number k. If (n-squared)+n+k is prime for all n=0,1,… up to square root of a third of k, then this number is prime for n=0,1, all the way up to n=k-2.

Unconventional problem that asks for proof that the numbers are prime, but a little gimmick gets us out of the conundrum. The solution looks like this:

Prime generator solution

The more intriguing part, of course, is to find such k.

I remembered from doing this problem that 41 fits, but any prime thereafter up to 150 fails. I later tried using computer program, hoping to test this from 2 up to 16 million. Here’s the code:

Prime generator code

And the output? 2,3,5,11,17,41. That’s all.

Surprising, isn’t it? Only that few numbers out of the enormous sea that contains millions of numbers work. To quench my thirst, I actually generated the primes (mainly for the 41-series since there are 40 primes emerging from nowhere.) Here they are, based on the 6 sequences defined above.

prime numbers

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