WON TOPIC 78

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[ October 3, 2000 ] Sets of three composites in bi-directional 'Sum Of Prime Factors' progression/retrogression I'd like to submit to the devoted number lovers the following rather hard puzzle ( catalogued as Sloane's A057874 ) in the hope of receiving the elusive 4 ^th set of three composites in bi-directional 'Sum Of Prime Factors' progression/retrogression. A mouthful, I am aware! Hence this jolly table which will clarify the concept better than any words can. Many more triplets have been found [ October, 2000 ] by Roberto Botrugno from Italy... read on! Click here to see how Roberto managed to find these remarkably large solutions

In the first set you'll notice no doubt six consecutive primes 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. 373 * 467 383 * 457 397 * 443 Common 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 entries A050780 - (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