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| | Puzzle 241. Highly imperfect primes |
 | | All multiples of 120 from 720 onwards have a cover value of over 120; so the cover is continuous from this point onwards, certainly to 30240 which eliminates all subsequent odd primes. |
 | | (720, 840, 1080, 1320, 1680, 2520, 3360, 4680, 6720, 10080, 17640, 30420) |
 | | From k = 720 = 2^4*3^2*5, the highly imperfect composite numbers always has a sigma big enough to beat all primes until the next highly imperfect composite (proved below), so the last highly imperfect prime is 719. |
| www.primepuzzles.net /puzzles/puzz_241.htm (1224 words) |
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