World!OfNumbers |
WON plate 78 | |
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[ I'd like to submit to the devoted number lovers the following rather hard puzzle
Click here to see how Roberto |

95 | 174191 | 298687992 | |||||||
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+ 5.19 = | – 7.17 = | + 373.467 = | – 383.457 = | + 2.2.2.3.179.251.277 = | – 2.2.17.53.179.463 = | ||||

119 | 175031 | 298688708 | |||||||

+ 7.17 = | – 11.13 = | + 383.457 = | – 397.443 = | + 2.2.17.53.179.463 = | – 2.2.2.2.11.19.179.499 = | ||||

143 | 175871 | 298689424 | |||||||

1 SOPF = 24 | 2 SOPF = 840 | 3 SOPF = 716 179 is a common factor! |

5, 7, 11, 13, 17 and 19.All the members of the first two sets are semi-primes i.e. having exactly two distinct factors. The third set has a common prime divisor > 2 to all members namely 179.Curious is also the loop taken counterclockwise of the middle digits of the factors of the second set starting from 443. It starts with a 4, then a 5, then a ... up to and then finally a 9 in factor 397. 3 73 * 4673 83 * 4573 97 * 443Common prime divisor of the members of the composite triplet (298687992, 298688708, 298689424) which are in a bi-directional 'sum of prime factors' (i.e., 716) progression/retrogression. Some OEIS entriesA050780 - (n + sopf_n = m) and (m - sopf_m = n). Sequence gives values of n. A050781 - (n + sopf_n = m) and (m - sopf_m = n). Sequence gives values of m. A057874 - Sets of three composites in bidirectional 'sum of prime factors' progression/retrogression. | |||

A000078 Prime Curios! Prime Puzzle Wikipedia 78 Le Nombre 78 Numberland 78 |

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