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:
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:
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.
anzoteh96 