okay, it seems i was trying to out think myself there; the associative
property of algebra is axiomatic and it declares that the order of operation won't matter.
(soop):
(3,5), (5,7), (7,9), (9,11), (11,13), (13,15), (15,17), (17,19), (19,21), (21,23), (23,25), (25,27), (27,29), (29,31), (31,33), (33,35), (35,37), (37,39), (39,41), (41,43), (43,45), (45,47), (47,49), (49,51), (51,53), (53,55), (55,57), (57,59), (59,61), (61,63), (63,65), (65,67), (67,69), (69,71), (71,73), (73,75), (75,77), (77,79), (79,81), (81,83), (83,85), (85,87), (87,89), (89,91), (91,93), (93,95), (95,97), (97,99),...etc
(soop) with 2/3 indicated as removable:
(3,5), (5,7), (7,9), (9,11), (11,13), (13,15), (15,17), (17,19), (19,21), (21,23), (23,25), (25,27), (27,29), (29,31), (31,33), (33,35), (35,37), (37,39), (39,41), (41,43), (43,45), (45,47), (47,49), (49,51), (51,53), (53,55), (55,57), (57,59), (59,61), (61,63), (63,65), (65,67), (67,69), (69,71), (71,73), (73,75), (75,77), (77,79), (79,81), (81,83), (83,85), (85,87), (87,89), (89,91), (91,93), (93,95), (95,97), (97,99),...etc
(soop) with 2/5 indicated as removable:
(3,5), (5,7), (7,9), (9,11), (11,13), (13,15), (15,17), (17,19), (19,21), (21,23), (23,25), (25,27), (27,29), (29,31), (31,33), (33,35), (35,37), (37,39), (39,41), (41,43), (43,45), (45,47), (47,49), (49,51), (51,53), (53,55), (55,57), (57,59), (59,61), (61,63), (63,65), (65,67), (67,69), (69,71), (71,73), (73,75), (75,77), (77,79), (79,81), (81,83), (83,85), (85,87), (87,89), (89,91), (91,93), (93,95), (95,97), (97,99),...etc
(soop) with 2/5 indicated as removable after 2/3 have been preindicated as removable:
(3,5), (5,7), (7,9), (9,11), (11,13), (13,15), (15,17), (17,19), (19,21), (21,23), (23,25), (25,27), (27,29), (29,31), (31,33), (33,35), (35,37), (37,39), (39,41), (41,43), (43,45), (45,47), (47,49), (49,51), (51,53), (53,55), (55,57), (57,59), (59,61), (61,63), (63,65), (65,67), (67,69), (69,71), (71,73), (73,75), (75,77), (77,79), (79,81), (81,83), (83,85), (85,87), (87,89), (89,91), (91,93), (93,95), (95,97), (97,99),...etc
with all pairs containing multiples of "3" removed, (soop) becomes 1/3 of what it began. removing all multiples of "5" (instead) would reduce (soop) to 60% (3/5) of what it had begun at. when applying the removal of "5" multiples after the "3" multiples had been extracted, the extraction process appears to be closer to 50% than to 40%.
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