Prime multiplication table

Prime multiplication table to 1000 (or slightly over...)


	7	11	13	17	19	23	29	31
7	49	-	-	-	-	-	-	-
11	77	121	-	-	-	-	-	-
13	91	143	169	-	-	-	-	-
17	119	187	221	289	-	-	-	-
19	133	209	247	323	361	-	-	-
23	161	253	299	391	437	529	-	-
29	203	319	377	493	551	667	841	-
31	217	341	403	527	589	713	899	961
39	259	407	481	629	703	851	1073
41	287	451	533	697	779	943
43	301	473	559	731	817	989
47	329	517	611	799	893	1081
53	371	583	689	901	1007
59	413	649	767	1003
61	427	671	793
67	469	737	871
71	497	781	923
73	511	803	949
79	553	869	1027
83	581	913
89	623	979
97	679	1067
101	707	1111
103	721
107	749
109	763
113	791
127	889
131	917
137	959
139	973
149 	1043
151 	1057


Any three-digit number not divisible by 2, 3, or 5

must either be one of the above numbers, or it must be



343 = 7 × 7 × 7

539 = 7 × 7 × 11

637 = 7 × 7 × 13

833 = 7 × 7 × 17

931 = 7 × 7 × 19



...the next smallest combination is 7 × 11 × 13 = 1001.

Prime tableaux

Tableau encodings to 2100:
(ON bits are composite)

0000: 00.04.08.81.92.24.43

0210: 60.54.0D.87.30.A8.9A

0420: 48.86.98.CF.34.34.23

0630: 44.65.5A.A9.19.B6.42

0840: E1.87.9A.95.95.38.4A

1050: 4B.84.AB.CD.55.64.3A

1260: F0.06.3F.D5.7A.E0.8B

1470: 40.DD.68.99.90.37.A3

1680: E2.CD.2B.A3.5D.77.02

1890: D5.CE.7C.A1.32.EC.C2

[4-bit must be ON 8-bit must be ON 1-bit must be ON 2-bit must be ON]

Each tableau of length 30 is encoded by two decimal digits, where an on bit in each digit means that the associated number is composite:

 First digit: 30n+1   30n+7   30n+11  30n+13

Second digit: 30n+17  30n+19  30n+23  30n+29

The colored digits above are characters where one of the bits is pre-determined due to a multiple of 7