Actual and conjectured gap count

Gap size : 24 (r=12)

Generated by program gapCounts : Wed Jul 16 16:27:39 2008

π(r,x) = actual gap count
L(r,x) = conjectured gap count
D(r,x) = L(r,x) - π(r,x)
S(r,x) = D(r,x)*ln(x)/x^½

x	π(r,x)	L(r,x)	D(r,x)	S(r,x)
1.0000e+02	0	0	0.00	0.00
2.0000e+02	0	-0	-0.00	-0.00
3.0000e+02	0	-0	-0.01	-0.00
4.0000e+02	0	-0	-0.01	-0.00
5.0000e+02	0	0	0.00	0.00
6.0000e+02	0	0	0.03	0.01
7.0000e+02	0	0	0.06	0.01
8.0000e+02	0	0	0.10	0.02
9.0000e+02	0	0	0.16	0.04
1.0000e+03	0	0	0.22	0.05
1.1000e+03	0	0	0.28	0.06
1.2000e+03	0	0	0.36	0.07
1.3000e+03	0	0	0.43	0.09
1.4000e+03	0	1	0.52	0.10
1.5000e+03	0	1	0.61	0.11
1.6000e+03	0	1	0.70	0.13
1.7000e+03	1	1	-0.20	-0.04
1.8000e+03	1	1	-0.10	-0.02
1.9000e+03	1	1	0.01	0.00
2.0000e+03	1	1	0.12	0.02
2.1000e+03	1	1	0.23	0.04
2.2000e+03	1	1	0.34	0.06
2.3000e+03	2	1	-0.54	-0.09
2.4000e+03	2	2	-0.42	-0.07
2.5000e+03	2	2	-0.29	-0.05
2.6000e+03	2	2	-0.17	-0.03
2.7000e+03	2	2	-0.04	-0.01
2.8000e+03	2	2	0.10	0.01
2.9000e+03	2	2	0.23	0.03
3.0000e+03	2	2	0.37	0.05
3.1000e+03	2	3	0.50	0.07
3.2000e+03	2	3	0.64	0.09
3.3000e+03	2	3	0.78	0.11
3.4000e+03	2	3	0.93	0.13
3.5000e+03	2	3	1.07	0.15
3.6000e+03	2	3	1.22	0.17
3.7000e+03	2	3	1.37	0.19
3.8000e+03	2	4	1.52	0.20
3.9000e+03	2	4	1.67	0.22
4.0000e+03	2	4	1.83	0.24
4.1000e+03	2	4	1.98	0.26
4.2000e+03	2	4	2.14	0.28
4.3000e+03	3	4	1.30	0.17
4.4000e+03	3	4	1.45	0.18
4.5000e+03	3	5	1.62	0.20
4.6000e+03	4	5	0.78	0.10
4.7000e+03	4	5	0.94	0.12
4.8000e+03	5	5	0.10	0.01
4.9000e+03	5	5	0.27	0.03
5.0000e+03	5	5	0.44	0.05
5.2000e+03	5	6	0.77	0.09
5.4000e+03	6	6	0.11	0.01
5.6000e+03	6	6	0.46	0.05
5.8000e+03	6	7	0.80	0.09
6.0000e+03	6	7	1.15	0.13
6.2000e+03	7	8	0.51	0.06
6.4000e+03	7	8	0.87	0.10
6.6000e+03	8	8	0.23	0.02
6.8000e+03	9	9	-0.41	-0.04
7.0000e+03	9	9	-0.04	-0.00
7.2000e+03	10	9	-0.67	-0.07
7.4000e+03	11	10	-1.30	-0.13
7.6000e+03	11	10	-0.92	-0.09
7.8000e+03	11	10	-0.54	-0.06
8.0000e+03	12	11	-1.16	-0.12
8.2000e+03	13	11	-1.78	-0.18
8.4000e+03	14	12	-2.39	-0.24
8.6000e+03	14	12	-2.01	-0.20
8.8000e+03	14	12	-1.62	-0.16
9.0000e+03	14	13	-1.22	-0.12
9.2000e+03	15	13	-1.83	-0.17
9.4000e+03	15	14	-1.44	-0.14
9.6000e+03	15	14	-1.04	-0.10
9.8000e+03	15	14	-0.64	-0.06
1.0000e+04	15	15	-0.24	-0.02
1.0500e+04	15	16	0.77	0.07
1.1000e+04	15	17	1.79	0.16
1.1500e+04	16	18	1.83	0.16
1.2000e+04	18	19	0.86	0.07
1.2500e+04	20	20	-0.09	-0.01
1.3000e+04	20	21	0.97	0.08
1.3500e+04	22	22	0.03	0.00
1.4000e+04	22	23	1.10	0.09
1.4500e+04	22	24	2.18	0.17
1.5000e+04	22	25	3.27	0.26
1.5500e+04	22	26	4.36	0.34
1.6000e+04	22	27	5.45	0.42
1.6500e+04	25	29	3.56	0.27
1.7000e+04	27	30	2.67	0.20
1.7500e+04	28	31	2.78	0.21
1.8000e+04	29	32	2.90	0.21
1.8500e+04	30	33	3.02	0.22
1.9000e+04	32	34	2.15	0.15
1.9500e+04	33	35	2.28	0.16
2.0000e+04	34	36	2.42	0.17
2.1000e+04	35	39	3.70	0.25
2.2000e+04	35	41	6.00	0.40
2.3000e+04	37	43	6.32	0.42
2.4000e+04	40	46	5.65	0.37
2.5000e+04	41	48	6.99	0.45
2.6000e+04	42	50	8.35	0.53
2.7000e+04	42	53	10.71	0.67
2.8000e+04	43	55	12.09	0.74
2.9000e+04	43	57	14.48	0.87
3.0000e+04	45	60	14.88	0.89
3.1000e+04	46	62	16.28	0.96
3.2000e+04	46	65	18.70	1.08
3.3000e+04	49	67	18.12	1.04
3.4000e+04	51	70	18.55	1.05
3.5000e+04	51	72	20.99	1.17
3.6000e+04	53	74	21.44	1.19
3.7000e+04	54	77	22.89	1.25
3.8000e+04	54	79	25.35	1.37
3.9000e+04	55	82	26.82	1.44
4.0000e+04	56	84	28.30	1.50
4.1000e+04	60	87	26.78	1.40
4.2000e+04	62	89	27.26	1.42
4.3000e+04	67	92	24.75	1.27
4.4000e+04	70	94	24.25	1.24
4.5000e+04	70	97	26.75	1.35
4.6000e+04	70	99	29.26	1.46
4.7000e+04	72	102	29.77	1.48
4.8000e+04	73	104	31.29	1.54
4.9000e+04	79	107	27.81	1.36
5.0000e+04	83	109	26.34	1.27
5.2000e+04	87	114	27.40	1.30
5.4000e+04	91	119	28.48	1.34
5.6000e+04	99	125	25.58	1.18
5.8000e+04	101	130	28.69	1.31
6.0000e+04	104	135	30.81	1.38
6.2000e+04	108	140	31.95	1.42
6.4000e+04	112	145	33.10	1.45
6.6000e+04	112	150	38.26	1.65
6.8000e+04	116	155	39.44	1.68
7.0000e+04	119	161	41.62	1.75
7.2000e+04	127	166	38.81	1.62
7.4000e+04	132	171	39.02	1.61
7.6000e+04	138	176	38.23	1.56
7.8000e+04	145	181	36.45	1.47
8.0000e+04	150	187	36.69	1.46
8.2000e+04	152	192	39.92	1.58
8.4000e+04	156	197	41.17	1.61
8.6000e+04	158	202	44.43	1.72
8.8000e+04	165	208	42.69	1.64
9.0000e+04	173	213	39.96	1.52
9.2000e+04	176	218	42.24	1.59
9.4000e+04	183	224	40.52	1.51
9.6000e+04	190	229	38.81	1.44
9.8000e+04	200	234	34.10	1.25
1.0000e+05	206	239	33.40	1.22
1.0500e+05	223	253	29.68	1.06
1.1000e+05	230	266	36.00	1.26
1.1500e+05	246	279	33.34	1.15
1.2000e+05	257	293	35.71	1.21
1.2500e+05	269	306	37.11	1.23
1.3000e+05	279	320	40.53	1.32
1.3500e+05	291	333	41.98	1.35
1.4000e+05	305	346	41.44	1.31
1.4500e+05	314	360	45.93	1.43
1.5000e+05	334	373	39.44	1.21
1.5500e+05	347	387	39.96	1.21
1.6000e+05	355	401	45.51	1.36
1.6500e+05	370	414	44.06	1.30
1.7000e+05	378	428	49.64	1.45
1.7500e+05	389	441	52.23	1.51
1.8000e+05	399	455	55.83	1.59
1.8500e+05	418	468	50.44	1.42
1.9000e+05	435	482	47.07	1.31
1.9500e+05	446	496	49.71	1.37
2.0000e+05	457	509	52.36	1.43
2.1000e+05	482	537	54.69	1.46
2.2000e+05	508	564	56.06	1.47
2.3000e+05	532	591	59.47	1.53
2.4000e+05	558	619	60.91	1.54
2.5000e+05	587	646	59.38	1.48
2.6000e+05	620	674	53.88	1.32
2.7000e+05	653	701	48.40	1.17
2.8000e+05	687	729	41.95	0.99
2.9000e+05	708	757	48.52	1.13
3.0000e+05	750	784	34.11	0.79
3.1000e+05	772	812	39.72	0.90
3.2000e+05	801	839	38.35	0.86
3.3000e+05	823	867	43.99	0.97
3.4000e+05	853	895	41.65	0.91
3.5000e+05	873	922	49.33	1.06
3.6000e+05	898	950	52.01	1.11
3.7000e+05	924	978	53.71	1.13
3.8000e+05	952	1005	53.42	1.11
3.9000e+05	984	1033	49.15	1.01
4.0000e+05	1013	1061	47.88	0.98
4.1000e+05	1039	1089	49.62	1.00
4.2000e+05	1061	1116	55.37	1.11
4.3000e+05	1080	1144	64.14	1.27
4.4000e+05	1110	1172	61.90	1.21
4.5000e+05	1130	1200	69.68	1.35
4.6000e+05	1156	1227	71.46	1.37
4.7000e+05	1193	1255	62.26	1.19
4.8000e+05	1214	1283	69.05	1.30
4.9000e+05	1247	1311	63.86	1.20
5.0000e+05	1278	1339	60.66	1.13
5.2000e+05	1331	1394	63.30	1.16
5.4000e+05	1396	1450	53.95	0.97
5.6000e+05	1457	1506	48.62	0.86
5.8000e+05	1510	1561	51.30	0.89
6.0000e+05	1559	1617	57.99	1.00
6.2000e+05	1609	1673	63.70	1.08
6.4000e+05	1672	1728	56.41	0.94
6.6000e+05	1728	1784	56.14	0.93
6.8000e+05	1796	1840	43.87	0.71
7.0000e+05	1860	1896	35.61	0.57
7.2000e+05	1917	1951	34.35	0.55
7.4000e+05	1976	2007	31.10	0.49
7.6000e+05	2042	2063	20.85	0.32
7.8000e+05	2106	2119	12.60	0.19
8.0000e+05	2160	2174	14.36	0.22
8.2000e+05	2217	2230	13.11	0.20
8.4000e+05	2261	2286	24.87	0.37
8.6000e+05	2322	2342	19.63	0.29
8.8000e+05	2379	2397	18.39	0.27
9.0000e+05	2440	2453	13.14	0.19
9.2000e+05	2491	2509	17.90	0.26
9.4000e+05	2542	2565	22.65	0.32
9.6000e+05	2588	2620	32.40	0.46
9.8000e+05	2633	2676	43.15	0.60
1.0000e+06	2682	2732	49.90	0.69
1.0500e+06	2825	2871	46.26	0.63
1.1000e+06	2971	3011	39.59	0.53
1.1500e+06	3108	3150	41.90	0.55
1.2000e+06	3257	3289	32.17	0.41
1.2500e+06	3400	3428	28.42	0.36
1.3000e+06	3538	3568	29.64	0.37
1.3500e+06	3671	3707	35.82	0.44
1.4000e+06	3811	3846	34.96	0.42
1.4500e+06	3951	3985	34.07	0.40
1.5000e+06	4088	4124	36.14	0.42
1.5500e+06	4231	4263	32.18	0.37
1.6000e+06	4396	4402	6.17	0.07
1.6500e+06	4525	4541	16.12	0.18
1.7000e+06	4653	4680	27.03	0.30
1.7500e+06	4797	4819	21.91	0.24
1.8000e+06	4934	4958	23.74	0.25
1.8500e+06	5073	5097	23.53	0.25
1.9000e+06	5216	5235	19.28	0.20
1.9500e+06	5361	5374	12.98	0.13
2.0000e+06	5522	5513	-9.35	-0.10
2.1000e+06	5790	5790	-0.14	-0.00
2.2000e+06	6056	6067	10.90	0.11
2.3000e+06	6332	6344	11.77	0.11
2.4000e+06	6602	6620	18.49	0.18
2.5000e+06	6887	6897	10.04	0.09
2.6000e+06	7161	7173	12.43	0.11
2.7000e+06	7409	7450	40.67	0.37
2.8000e+06	7698	7726	27.74	0.25
2.9000e+06	7960	8002	41.67	0.36
3.0000e+06	8227	8277	50.43	0.43
3.1000e+06	8517	8553	36.05	0.31
3.2000e+06	8793	8829	35.52	0.30
3.3000e+06	9067	9104	36.84	0.30
3.4000e+06	9323	9379	56.02	0.46
3.5000e+06	9605	9654	49.05	0.40
3.6000e+06	9856	9929	72.94	0.58
3.7000e+06	10139	10204	64.70	0.51
3.8000e+06	10429	10478	49.31	0.38
3.9000e+06	10698	10753	54.79	0.42
4.0000e+06	10967	11027	60.14	0.46
4.1000e+06	11265	11301	36.35	0.27
4.2000e+06	11548	11575	27.43	0.20
4.3000e+06	11841	11849	8.39	0.06
4.4000e+06	12115	12123	8.22	0.06
4.5000e+06	12394	12397	2.92	0.02
4.6000e+06	12649	12670	21.50	0.15
4.7000e+06	12944	12944	-0.04	-0.00
4.8000e+06	13207	13217	10.29	0.07
4.9000e+06	13441	13491	49.51	0.34
5.0000e+06	13698	13764	65.61	0.45
5.2000e+06	14218	14309	91.46	0.62
5.4000e+06	14767	14855	87.86	0.59
5.6000e+06	15282	15400	117.82	0.77
5.8000e+06	15862	15944	82.35	0.53
6.0000e+06	16414	16488	74.45	0.47
6.2000e+06	16952	17032	80.14	0.50
6.4000e+06	17506	17575	69.43	0.43
6.6000e+06	18064	18118	54.32	0.33
6.8000e+06	18558	18661	102.83	0.62
7.0000e+06	19072	19203	130.95	0.78
7.2000e+06	19636	19745	108.71	0.64
7.4000e+06	20150	20286	136.10	0.79
7.6000e+06	20695	20827	132.13	0.76
7.8000e+06	21187	21368	180.82	1.03
8.0000e+06	21740	21908	168.15	0.94
8.2000e+06	22287	22448	161.16	0.90
8.4000e+06	22845	22988	142.83	0.79
8.6000e+06	23412	23527	115.17	0.63
8.8000e+06	23988	24066	78.20	0.42
9.0000e+06	24504	24605	100.91	0.54
9.2000e+06	25009	25143	134.31	0.71
9.4000e+06	25586	25681	95.40	0.50
9.6000e+06	26105	26219	114.20	0.59
9.8000e+06	26597	26757	159.71	0.82
1.0000e+07	27170	27294	123.92	0.63
1.0500e+07	28499	28636	136.72	0.68
1.1000e+07	29835	29976	140.79	0.69
1.1500e+07	31178	31314	136.22	0.65
1.2000e+07	32505	32651	146.04	0.69
1.2500e+07	33832	33986	154.32	0.71
1.3000e+07	35214	35320	106.10	0.48
1.3500e+07	36521	36652	131.43	0.59
1.4000e+07	37853	37983	130.36	0.57
1.4500e+07	39141	39313	171.92	0.74
1.5000e+07	40505	40641	136.15	0.58
1.5500e+07	41768	41968	200.10	0.84
1.6000e+07	43148	43294	145.79	0.60
1.6500e+07	44425	44618	193.26	0.79
1.7000e+07	45765	45942	176.54	0.71
1.7500e+07	47104	47264	159.66	0.64
1.8000e+07	48417	48585	167.64	0.66
1.8500e+07	49730	49905	174.52	0.68
1.9000e+07	51054	51223	169.31	0.65
1.9500e+07	52360	52541	181.05	0.69
2.0000e+07	53675	53858	182.75	0.69
2.1000e+07	56291	56488	197.15	0.73
2.2000e+07	58964	59115	150.66	0.54
2.3000e+07	61498	61737	239.44	0.85
2.4000e+07	64069	64357	287.63	1.00
2.5000e+07	66738	66972	234.36	0.80
2.6000e+07	69335	69585	249.76	0.84
2.7000e+07	72057	72194	136.93	0.45
2.8000e+07	74700	74800	99.99	0.32
2.9000e+07	77373	77403	30.02	0.10
3.0000e+07	79967	80003	36.13	0.11
3.1000e+07	82585	82600	15.40	0.05
3.2000e+07	85249	85195	-54.09	-0.17
3.3000e+07	87869	87787	-82.26	-0.25
3.4000e+07	90455	90376	-79.04	-0.24
3.5000e+07	93069	92963	-106.36	-0.31
3.6000e+07	95633	95547	-86.15	-0.25
3.7000e+07	98167	98129	-38.35	-0.11
3.8000e+07	100818	100708	-109.91	-0.31
3.9000e+07	103390	103285	-104.76	-0.29
4.0000e+07	105919	105860	-58.85	-0.16
4.1000e+07	108413	108433	19.86	0.05
4.2000e+07	111036	111003	-32.57	-0.09
4.3000e+07	113601	113572	-29.10	-0.08
4.4000e+07	116232	116138	-93.67	-0.25
4.5000e+07	118819	118703	-116.26	-0.31
4.6000e+07	121412	121265	-146.82	-0.38
4.7000e+07	123980	123826	-154.30	-0.40
4.8000e+07	126650	126384	-265.68	-0.68
4.9000e+07	129106	128941	-164.91	-0.42
5.0000e+07	131723	131496	-226.96	-0.57
5.2000e+07	136747	136601	-146.39	-0.36
5.4000e+07	141908	141698	-209.72	-0.51
5.6000e+07	147026	146789	-236.69	-0.56
5.8000e+07	152158	151874	-284.11	-0.67
6.0000e+07	157208	156952	-255.75	-0.59
6.2000e+07	162288	162025	-263.42	-0.60
6.4000e+07	167412	167091	-320.95	-0.72
6.6000e+07	172491	172152	-339.16	-0.75
6.8000e+07	177586	177207	-378.89	-0.83
7.0000e+07	182594	182257	-336.99	-0.73
7.2000e+07	187622	187302	-320.31	-0.68
7.4000e+07	192682	192341	-340.72	-0.72
7.6000e+07	197723	197376	-347.09	-0.72
7.8000e+07	202806	202406	-400.29	-0.82
8.0000e+07	207737	207431	-306.21	-0.62
8.2000e+07	212748	212451	-296.73	-0.60
8.4000e+07	217781	217467	-313.75	-0.62
8.6000e+07	222887	222479	-408.17	-0.80
8.8000e+07	227867	227486	-380.89	-0.74
9.0000e+07	232799	232489	-309.82	-0.60
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