What is the maximal number of semiprimes among 100 consecutive numbers? 38?
We might never know. Considering only divisibility by small semiprimes, one can find a sequence of only 69 consecutive numbers, 39 of which are not divisible by any semiprime <= 69. For examples, 42117702927300*N + 13684292903, 05, 06, 07, 09, 11, 13, 14, 15, 17, 18, 21, 23, 26, 27, 29, 31, 33, 35, 38, 39, 41, 42, 43, 45, 47, 49, 51, 53, 54, 57, 59, 61, 62, 63, 66, 67, 69, 71. Maybe for some choice of N, all of these are semiprime. But I despair of finding such an N. The minimum span (last - first + 1) of N semiprimes goes 1,2,3,5,6,7,9,11,13,14,16,17,19,21,... or does it? If that's correct, it (or the incremented sequence) would surely be in the OEIS: where did I go wrong? How does the density of semiprimes vary with the size? -- Don Reble djr@nk.ca