I'm faced with factoring many CONSECUTIVE large integers. What are the speediest algorithms available for factoring ALL the integers between (say) 10^N + 1 and 10^(N+1) + 1, for N = 10, 11, 12, 13, 14, 15, ... ? For each such N, how much time T(N) would be required to factor these integers? Would the same algorithm be used for each N ? Can some of these factorizations be accomplished on a Mac at home ?
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