UNSOLVED PROBLEMS

In Number Theory, Logic, and Cryptography

Legendre’s Conjecture

 

Between 13² (=169) and 14² (=196) there are five primes (173, 179, 181, 191, and 193); between 30² (=900) and 31² (=961) there are eight primes (907, 911, 919, 929, 937, 941, 947, and 953); between 35² (=1225) and 36² (=1296) there are ten primes (1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, and 1291).

The problem is to prove Legendre's Conjecture, which states that there is at least one prime number between every pair of consecutive squares, or find a counter-example.

 

For further information, please see:

[1] http://mathworld.wolfram.com/LegendresConjecture.html

[2] http://en.wikipedia.org/wiki/Legendre%27s_conjecture

[3] http://arxiv.org/PS_cache/arxiv/pdf/0811/0811.4451v2.pdf

 

You can check for contributions to this problem on the solutions page.

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