all positive integers other than 15. The 290 theorem says a positive definite integral quadratic form is universal if it takes the numbers from 1 to 290 as values. A more precise version states that, if an integer valued integral quadratic form represents all the numbers 1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 34, 35, 37, 42, 58, 93, 110, 145, 203, 290 , then it represents all positive integers, and for each of these 29 numbers, there is such a quadratic form representing all other 28 positive integers with the exception of this one number. Bhargava has found analogous criteria for a quadratic form with integral matrix to represent all primes (the set {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 67, 73} ) and for such a quadratic form to represent all positive odd integers (the set {1, 3, 5, 7, 11, 15, 33} ). Expository accounts of these result have been written by Hahn and Moon (who provides proofs). References Additive number theory Theorems in number theory Quadratic forms