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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) A generalized arithmetic progression of primes (a GAP) is a set of integers of the form a + n_{1}b_{1} + n_{2}b_{2} + ... + n_{d}b_{d}with a, b_{1}, b_{2}, ..., b_{d} fixed; and the n's run through some range. The table below shows the smallest 2byk GAP's (those with the least last term) for small k. When k is 9, the largest term is 5179. k GAP Last Term 2 3+8i+2j 13 3 7+24i+6j 43 4 5+36i+6j 59 5 11+96i+30j 227 6 11+42i+60j 353 7 47+132i+210j 1439 8 199+3300i+210j 4969 9 199+3300i+210j 5179
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