UNSOLVED PROBLEMS

In Number Theory, Logic, and Cryptography

Legendre痴 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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