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	II: TRIM NUMBERS
	The significance of the Prime Number Generating Theorem is seen in the
	following algorithm.
	We define Trim numbers recursively by t(1) = 2, and t(n+1) = t(n) + d(n),
	where p(i) is the i'th prime and:
		(1) d(1) = 1, and a(2, 1) = 1 is the only element in the 2nd array;
		(2) d(n) is the smallest even integer that does not occur in the
			n'th array {a(n, 1), …, a(n, n-1)};
		(3)  j is selected so that 0 ≤ a(n+1, i) = (a(n, i) - d(n) + j*p(i) < p(i)
			for all 0 < i ≤ (n-1);
	It follows that the Trim number t(n+1) is, thus, a prime unless all its prime divisors
	are less than d(n).
	THE TRIM NUMBER ALGORITHM
	The following illustrates how Trim numbers are generated sequentially.
	n	t(n)
	1	2	2	3	5	7	11	13	17	19	23		29	31	37	41	43	47	53	59	61	67	71	73	79	83	89	97	101	103	107	109	113		127	131	137	139		149	151	157	163	167	173	179	181		191	193	197	199	211
	2	3	1	2	5
	3	5	1	4	2	7
	4	7	1	2	3	4	11
	5	11	1	1	4	3	2	13
	6	13	1	2	2	1	9	4	17
	7	17	1	1	3	4	5	9	2	19
	8	19	1	2	1	2	3	7	15	4	23
	9	23	1	1	2	5	10	3	11	15	4	27
	10	27	1	0	3	1	6	12	7	11	19	2	29	<== (1)
	11	29	1	1	1	6	4	10	5	9	17		2	31
	12	31	1	2	4	4	2	8	3	7	15		27	6	37
	13	37	1	2	3	5	7	2	14	1	9		21	25	4	41
	14	41	1	1	4	1	3	11	10	16	5		17	21	33	2	43
	15	43	1	2	2	6	1	9	8	14	3		15	19	31	39	4	47
	16	47	1	1	3	2	8	5	4	10	22		11	15	27	35	39	6	53
	17	53	1	1	2	3	2	12	15	4	16		5	9	21	29	33	41	6	59
	18	59	1	1	1	4	7	6	9	17	10		28	3	15	23	27	35	47	2	61
	19	61	1	2	4	2	5	4	7	15	8		26	1	13	21	25	33	45	57	6	67
	20	67	1	2	3	3	10	11	1	9	2		20	26	7	15	19	27	39	51	55	4	71
	21	71	1	1	4	6	6	7	14	5	21		16	22	3	11	15	23	35	47	51	63	2	73
	22	73	1	2	2	4	4	5	12	3	19		14	20	1	9	13	21	33	45	49	61	69	6	79
	23	79	1	2	1	5	9	12	6	16	13		8	14	32	3	7	15	27	39	43	55	63	67	4	83
	24	83	1	1	2	1	5	8	2	12	9		4	10	28	40	3	11	23	35	39	51	59	63	73	6	89
	25	89	1	1	1	2	10	2	13	6	3		27	4	22	34	40	5	17	29	33	45	53	57	67	77	8	97
	26	97	1	2	3	1	2	7	5	17	18		19	27	14	26	32	44	9	21	25	37	45	49	59	69	81	4	101
	27	101	1	1	4	4	9	3	1	13	14		15	23	10	22	28	40	5	17	21	33	41	45	55	65	77	93	2	103
	28	103	1	2	2	2	7	1	16	11	12		13	21	8	20	26	38	3	15	19	31	39	43	53	63	75	91	99	4	107
	29	107	1	1	3	5	3	10	12	7	8		9	17	4	16	22	34	52	11	15	27	35	39	49	59	71	87	95	99	2	109
	30	109	1	2	1	3	1	8	10	5	6		7	15	2	14	20	32	50	9	13	25	33	37	47	57	69	85	93	97	105	4	113
	31	113	1	1	2	6	8	4	6	1	2		3	11	35	10	16	28	46	5	9	21	29	33	43	53	65	81	89	93	101	105	12	125
	32	125	1	1	0	1	7	5	11	8	13		20	30	23	39	4	16	34	52	58	9	17	21	31	41	53	69	77	81	89	93	101	2	127	<== (2)
	33	127	1	2	3	6	5	3	9	6	11		18	28	21	37	2	14	32	50	56	7	15	19	29	39	51	67	75	79	87	91	99		4	131
	34	131	1	1	4	2	1	12	5	2	7		14	24	17	33	41	10	28	46	52	3	11	15	25	35	47	63	71	75	83	87	95		123	6	137
	35	137	1	1	3	3	6	6	16	15	1		8	18	11	27	35	4	22	40	46	64	5	9	19	29	41	57	65	69	77	81	89		117	125	2	139
	36	139	1	2	1	1	4	4	14	13	22		6	16	9	25	33	2	20	38	44	62	3	7	17	27	39	55	63	67	75	79	87		115	123	135	8	147
	37	147	1	0	3	0	7	9	6	5	14		27	8	1	17	25	41	12	30	36	54	66	72	9	19	31	47	55	59	67	71	79		107	115	127	131	2	149	<== (3)
	38	149	1	1	1	5	5	7	4	3	12		25	6	36	15	23	39	10	28	34	52	64	70	7	17	29	45	53	57	65	69	77		105	113	125	129		2	151
	39	151	1	2	4	3	3	5	2	1	10		23	4	34	13	21	37	8	26	32	50	62	68	5	15	27	43	51	55	63	67	75		103	111	123	127		147	6	157
	40	157	1	2	3	4	8	12	13	14	4		17	29	28	7	15	31	2	20	26	44	56	62	78	9	21	37	45	49	57	61	69		97	105	117	121		141	145	6	163
	41	163	1	2	2	5	2	6	7	8	21		11	23	22	1	9	25	49	14	20	38	50	56	72	3	15	31	39	43	51	55	63		91	99	111	115		135	139	151	4	167
	42	167	1	1	3	1	9	2	3	4	17		7	19	18	38	5	21	45	10	16	34	46	52	68	82	11	27	35	39	47	51	59		87	95	107	111		131	135	147	159	6	173
	43	173	1	1	2	2	3	9	14	17	11		1	13	12	32	42	15	39	4	10	28	40	46	62	76	5	21	29	33	41	45	53		81	89	101	105		125	129	141	153	161	6	179
	44	179	1	1	1	3	8	3	8	11	5		24	7	6	26	36	9	33	57	4	22	34	40	56	70	88	15	23	27	35	39	47		75	83	95	99		119	123	135	147	155	167	2	181
	45	181	1	2	4	1	6	1	6	9	3		22	5	4	24	34	7	31	55	2	20	32	38	54	68	86	13	21	25	33	37	45		73	81	93	97		117	121	133	145	153	165	177	8	189
	46	189	1	0	1	0	9	6	15	1	18		14	28	33	16	26	46	23	47	55	12	24	30	46	60	78	5	13	17	25	29	37		65	73	85	89		109	113	125	137	145	157	169	173	2	191	<== (4)
	47	191	1	1	4	5	7	4	13	18	16		12	26	31	14	24	44	21	45	53	10	22	28	44	58	76	3	11	15	23	27	35		63	71	83	87		107	111	123	135	143	155	167	171		2	193
	48	193	1	2	2	3	5	2	11	16	14		10	24	29	12	22	42	19	43	51	8	20	26	42	56	74	1	9	13	21	25	33		61	69	81	85		105	109	121	133	141	153	165	169		189	4	197
	49	197	1	1	3	6	1	11	7	12	10		6	20	25	8	18	38	15	39	47	4	16	22	38	52	70	94	5	9	17	21	29		57	65	77	81		101	105	117	129	137	149	161	165		185	189	2	199
	50	199	1	2	1	4	10	9	5	10	8		4	18	23	6	16	36	13	37	45	2	14	20	36	50	68	92	3	7	15	19	27		55	63	75	79		99	103	115	127	135	147	159	163		183	187	195	12	211
	Summary:				Total Trim numbers generated: 50; Primes: 46; Composites: 4.
					(1) Trim composite 27 = 3*3*3
					(2) Trim composite 125 = 5*5*5
					(3) Trim composite 147 = 3*7*7
					(4) Trim composite 189 = 3*3*3*7
	A Trim Number theorem …
	Theorem:			For all n > 1, t(n) < n*n
	Proof:			t(n) = {t(n-1) + d(n-1)}
				d(n-1) < 2(n-1)
				t(n) < {t(n-1) + 2(n-1)}
				t(n) < [{t(n-2) + 2(n-2)} + 2(n-1)]
				t(n) < {2 + 2(n-1) + 2(n-2) + … + 2(1)}
				t(n) < [2 + 2{(n-1)n/2}]
				t(n) < (n*n - n + 2)