[sdmzsnne] unobvious composites

a multiplication table between pairs of small prime numbers:

*	13	17	19	23	29	31	37	41	43
13	169	221	247	299	377	403	481	533	559
17	221	289	323	391	493	527	629	697	731
19	247	323	361	437	551	589	703	779	817
23	299	391	437	529	667	713	851	943	989
29	377	493	551	667	841	899	1073	1189	1247
31	403	527	589	713	899	961	1147	1271	1333
37	481	629	703	851	1073	1147	1369	1517	1591
41	533	697	779	943	1189	1271	1517	1681	1763
43	559	731	817	989	1247	1333	1591	1763	1849

divisibility by 2, 3, 5, 11 can be checked by well known rules, and 7 can be checked by short division (requiring effort similar to checks of 3 and 11), so the table starts at 13.  it stops at the last prime (43) whose square is less than the cube of the smallest: (13^3 = 2197) < (47^2 = 2209).

45 table entries, after commutativity.

there are many non-obvious composites (without easy divisibility check) of similar size as entries in the table but not in the table above.  the smallest is 13*47 = 611, so the table contains all non-obvious composites only up to 610.

with that in mind, better is a list rather than a table.  below are the 43 non-obvious composites less than 1000:

169 = 13 * 13
221 = 13 * 17
247 = 13 * 19
289 = 17 * 17
299 = 13 * 23
323 = 17 * 19
361 = 19 * 19
377 = 13 * 29
391 = 17 * 23
403 = 13 * 31
437 = 19 * 23
481 = 13 * 37
493 = 17 * 29
527 = 17 * 31
529 = 23 * 23
533 = 13 * 41
551 = 19 * 29
559 = 13 * 43
589 = 19 * 31
611 = 13 * 47
629 = 17 * 37
667 = 23 * 29
689 = 13 * 53
697 = 17 * 41
703 = 19 * 37
713 = 23 * 31
731 = 17 * 43
767 = 13 * 59
779 = 19 * 41
793 = 13 * 61
799 = 17 * 47
817 = 19 * 43
841 = 29 * 29
851 = 23 * 37
871 = 13 * 67
893 = 19 * 47
899 = 29 * 31
901 = 17 * 53
923 = 13 * 71
943 = 23 * 41
949 = 13 * 73
961 = 31 * 31
989 = 23 * 43

the next entry would be 1003 = 17 * 59.

for divisibility and prime factorization, you only need to know one of the factors, probably the smaller one.

previously, on memorizing the primes less than 1000.  memorizing the composites this way seems competitive and also gets you useful prime factorization.