---+-----+-----
 1 |  1  | 28
---+-----+-----
 2 | 29  | 46
---+-----+-----
 3 | 47  |{56}
---+-----+-----
 4 |{57} | 61
---+-----+-----
 5 | 62  | 82
---+-----+-----
 6 | 83  | 94
---+-----+-----
 7 | 95  | 99
---+-----+-----
 8 |{100}|{123}
---+-----+-----

Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles' proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three. (Clay Institute).