Actual and conjectured gap count

Gap size : 12 (r=6)

Generated by program gapCounts : Wed Jul 16 14:45:18 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	-1	-0.56	-0.26
2.0000e+02	0	-0	-0.02	-0.01
3.0000e+02	2	1	-1.18	-0.39
4.0000e+02	2	2	-0.21	-0.06
5.0000e+02	3	3	-0.17	-0.05
6.0000e+02	4	4	-0.09	-0.02
7.0000e+02	6	5	-0.98	-0.24
8.0000e+02	6	6	0.16	0.04
9.0000e+02	7	7	0.30	0.07
1.0000e+03	7	8	1.45	0.32
1.1000e+03	8	10	1.62	0.34
1.2000e+03	8	11	2.78	0.57
1.3000e+03	10	12	1.95	0.39
1.4000e+03	11	13	2.13	0.41
1.5000e+03	12	14	2.30	0.43
1.6000e+03	15	15	0.48	0.09
1.7000e+03	15	17	1.66	0.30
1.8000e+03	16	18	1.84	0.32
1.9000e+03	18	19	1.01	0.18
2.0000e+03	19	20	1.19	0.20
2.1000e+03	20	21	1.37	0.23
2.2000e+03	21	23	1.55	0.25
2.3000e+03	21	24	2.73	0.44
2.4000e+03	22	25	2.90	0.46
2.5000e+03	24	26	2.08	0.33
2.6000e+03	25	27	2.25	0.35
2.7000e+03	26	28	2.43	0.37
2.8000e+03	27	30	2.60	0.39
2.9000e+03	27	31	3.77	0.56
3.0000e+03	28	32	3.94	0.58
3.1000e+03	30	33	3.11	0.45
3.2000e+03	31	34	3.28	0.47
3.3000e+03	33	35	2.44	0.34
3.4000e+03	35	37	1.61	0.22
3.5000e+03	35	38	2.77	0.38
3.6000e+03	37	39	1.94	0.26
3.7000e+03	38	40	2.10	0.28
3.8000e+03	38	41	3.26	0.44
3.9000e+03	38	42	4.42	0.58
4.0000e+03	39	44	4.58	0.60
4.1000e+03	41	45	3.73	0.48
4.2000e+03	42	46	3.89	0.50
4.3000e+03	42	47	5.04	0.64
4.4000e+03	42	48	6.20	0.78
4.5000e+03	44	49	5.35	0.67
4.6000e+03	45	50	5.50	0.68
4.7000e+03	46	52	5.65	0.70
4.8000e+03	47	53	5.80	0.71
4.9000e+03	49	54	4.94	0.60
5.0000e+03	50	55	5.09	0.61
5.2000e+03	52	57	5.38	0.64
5.4000e+03	54	60	5.66	0.66
5.6000e+03	56	62	5.94	0.69
5.8000e+03	56	64	8.22	0.94
6.0000e+03	58	66	8.49	0.95
6.2000e+03	60	69	8.76	0.97
6.4000e+03	61	71	10.02	1.10
6.6000e+03	61	73	12.28	1.33
6.8000e+03	63	76	12.53	1.34
7.0000e+03	64	78	13.78	1.46
7.2000e+03	68	80	12.03	1.26
7.4000e+03	69	82	13.27	1.37
7.6000e+03	70	85	14.51	1.49
7.8000e+03	72	87	14.74	1.50
8.0000e+03	77	89	11.97	1.20
8.2000e+03	79	91	12.20	1.21
8.4000e+03	80	93	13.43	1.32
8.6000e+03	82	96	13.65	1.33
8.8000e+03	84	98	13.87	1.34
9.0000e+03	87	100	13.08	1.26
9.2000e+03	91	102	11.29	1.07
9.4000e+03	93	104	11.50	1.08
9.6000e+03	95	107	11.70	1.10
9.8000e+03	100	109	8.90	0.83
1.0000e+04	105	111	6.10	0.56
1.0500e+04	111	117	5.58	0.50
1.1000e+04	115	122	7.05	0.63
1.1500e+04	123	127	4.50	0.39
1.2000e+04	128	133	4.93	0.42
1.2500e+04	132	138	6.34	0.53
1.3000e+04	139	144	4.74	0.39
1.3500e+04	144	149	5.12	0.42
1.4000e+04	145	154	9.49	0.77
1.4500e+04	148	160	11.84	0.94
1.5000e+04	151	165	14.18	1.11
1.5500e+04	157	171	13.50	1.05
1.6000e+04	164	176	11.82	0.90
1.6500e+04	167	181	14.12	1.07
1.7000e+04	175	186	11.40	0.85
1.7500e+04	178	192	13.68	1.01
1.8000e+04	186	197	10.94	0.80
1.8500e+04	195	202	7.19	0.52
1.9000e+04	202	207	5.44	0.39
1.9500e+04	206	213	6.66	0.47
2.0000e+04	214	218	3.88	0.27
2.1000e+04	230	228	-1.71	-0.12
2.2000e+04	238	239	0.66	0.04
2.3000e+04	251	249	-2.01	-0.13
2.4000e+04	264	259	-4.72	-0.31
2.5000e+04	276	270	-6.46	-0.41
2.6000e+04	285	280	-5.24	-0.33
2.7000e+04	297	290	-7.04	-0.44
2.8000e+04	305	300	-4.88	-0.30
2.9000e+04	317	310	-6.75	-0.41
3.0000e+04	327	320	-6.65	-0.40
3.1000e+04	339	330	-8.58	-0.50
3.2000e+04	344	340	-3.54	-0.21
3.3000e+04	354	350	-3.52	-0.20
3.4000e+04	363	360	-2.52	-0.14
3.5000e+04	374	370	-3.56	-0.20
3.6000e+04	390	380	-9.61	-0.53
3.7000e+04	404	390	-13.69	-0.75
3.8000e+04	410	400	-9.79	-0.53
3.9000e+04	419	410	-8.92	-0.48
4.0000e+04	426	420	-6.07	-0.32
4.1000e+04	441	430	-11.23	-0.59
4.2000e+04	450	440	-10.42	-0.54
4.3000e+04	461	449	-11.63	-0.60
4.4000e+04	468	459	-8.86	-0.45
4.5000e+04	485	469	-16.11	-0.81
4.6000e+04	492	479	-13.38	-0.67
4.7000e+04	502	488	-13.66	-0.68
4.8000e+04	510	498	-11.97	-0.59
4.9000e+04	522	508	-14.29	-0.70
5.0000e+04	534	517	-16.63	-0.80
5.2000e+04	553	537	-16.35	-0.78
5.4000e+04	574	556	-18.14	-0.85
5.6000e+04	587	575	-12.00	-0.55
5.8000e+04	603	594	-8.91	-0.41
6.0000e+04	615	613	-1.89	-0.08
6.2000e+04	629	632	3.08	0.14
6.4000e+04	641	651	10.00	0.44
6.6000e+04	651	670	18.86	0.81
6.8000e+04	678	689	10.68	0.46
7.0000e+04	692	707	15.44	0.65
7.2000e+04	720	726	6.15	0.26
7.4000e+04	743	745	1.82	0.08
7.6000e+04	766	763	-2.55	-0.10
7.8000e+04	782	782	0.03	0.00
8.0000e+04	798	801	2.57	0.10
8.2000e+04	819	819	0.06	0.00
8.4000e+04	840	838	-2.48	-0.10
8.6000e+04	859	856	-3.07	-0.12
8.8000e+04	876	874	-1.69	-0.06
9.0000e+04	890	893	2.65	0.10
9.2000e+04	903	911	7.95	0.30
9.4000e+04	917	929	12.22	0.46
9.6000e+04	936	947	11.45	0.42
9.8000e+04	950	966	15.65	0.57
1.0000e+05	964	984	19.81	0.72
1.0500e+05	1013	1029	16.08	0.57
1.1000e+05	1049	1074	25.15	0.88
1.1500e+05	1091	1119	28.04	0.96
1.2000e+05	1131	1164	32.75	1.11
1.2500e+05	1172	1208	36.29	1.20
1.3000e+05	1223	1253	29.67	0.97
1.3500e+05	1270	1297	26.89	0.86
1.4000e+05	1316	1341	24.97	0.79
1.4500e+05	1356	1385	28.90	0.90
1.5000e+05	1399	1429	29.69	0.91
1.5500e+05	1435	1472	37.35	1.13
1.6000e+05	1480	1516	35.88	1.07
1.6500e+05	1528	1559	31.28	0.93
1.7000e+05	1561	1603	41.57	1.21
1.7500e+05	1615	1646	30.73	0.89
1.8000e+05	1657	1689	31.79	0.91
1.8500e+05	1698	1732	33.74	0.95
1.9000e+05	1740	1775	34.57	0.96
1.9500e+05	1777	1817	40.31	1.11
2.0000e+05	1821	1860	38.95	1.06
2.1000e+05	1907	1945	37.93	1.01
2.2000e+05	1991	2030	38.54	1.01
2.3000e+05	2079	2114	34.79	0.90
2.4000e+05	2157	2198	40.71	1.03
2.5000e+05	2251	2281	30.31	0.75
2.6000e+05	2316	2365	48.60	1.19
2.7000e+05	2392	2448	55.60	1.34
2.8000e+05	2472	2530	58.31	1.38
2.9000e+05	2555	2613	57.76	1.35
3.0000e+05	2631	2695	63.94	1.47
3.1000e+05	2727	2777	49.87	1.13
3.2000e+05	2820	2859	38.55	0.86
3.3000e+05	2898	2940	42.01	0.93
3.4000e+05	2991	3021	30.23	0.66
3.5000e+05	3069	3102	33.24	0.72
3.6000e+05	3160	3183	23.03	0.49
3.7000e+05	3248	3264	15.61	0.33
3.8000e+05	3329	3344	15.00	0.31
3.9000e+05	3401	3424	23.19	0.48
4.0000e+05	3487	3504	17.19	0.35
4.1000e+05	3565	3584	19.01	0.38
4.2000e+05	3637	3664	26.65	0.53
4.3000e+05	3710	3743	33.12	0.66
4.4000e+05	3782	3822	40.41	0.79
4.5000e+05	3842	3902	59.54	1.16
4.6000e+05	3909	3981	71.51	1.37
4.7000e+05	3989	4059	70.32	1.34
4.8000e+05	4078	4138	59.97	1.13
4.9000e+05	4147	4216	69.48	1.30
5.0000e+05	4237	4295	57.84	1.07
5.2000e+05	4401	4451	50.12	0.91
5.4000e+05	4551	4607	55.86	1.00
5.6000e+05	4699	4762	63.06	1.12
5.8000e+05	4852	4917	64.76	1.13
6.0000e+05	5018	5071	52.97	0.91
6.2000e+05	5183	5225	41.71	0.71
6.4000e+05	5335	5378	42.99	0.72
6.6000e+05	5487	5531	43.83	0.72
6.8000e+05	5646	5683	37.25	0.61
7.0000e+05	5775	5835	60.26	0.97
7.2000e+05	5922	5987	64.87	1.03
7.4000e+05	6111	6138	27.09	0.43
7.6000e+05	6261	6289	27.94	0.43
7.8000e+05	6394	6439	45.43	0.70
8.0000e+05	6532	6590	57.56	0.87
8.2000e+05	6670	6739	69.35	1.04
8.4000e+05	6822	6889	66.81	0.99
8.6000e+05	6973	7038	64.94	0.96
8.8000e+05	7122	7187	64.76	0.94
9.0000e+05	7276	7335	59.26	0.86
9.2000e+05	7427	7483	56.47	0.81
9.4000e+05	7567	7631	64.38	0.91
9.6000e+05	7709	7779	70.00	0.98
9.8000e+05	7863	7926	63.34	0.88
1.0000e+06	8005	8073	68.41	0.95
1.0500e+06	8373	8440	66.92	0.91
1.1000e+06	8714	8805	90.84	1.20
1.1500e+06	9081	9168	87.25	1.14
1.2000e+06	9435	9530	95.23	1.22
1.2500e+06	9789	9891	101.83	1.28
1.3000e+06	10162	10250	88.13	1.09
1.3500e+06	10506	10608	102.17	1.24
1.4000e+06	10862	10965	103.00	1.23
1.4500e+06	11204	11321	116.69	1.37
1.5000e+06	11539	11675	136.26	1.58
1.5500e+06	11899	12029	129.76	1.49
1.6000e+06	12228	12381	153.22	1.73
1.6500e+06	12583	12733	149.70	1.67
1.7000e+06	12934	13083	149.20	1.64
1.7500e+06	13289	13433	143.78	1.56
1.8000e+06	13681	13781	100.46	1.08
1.8500e+06	14040	14129	89.26	0.95
1.9000e+06	14425	14476	51.21	0.54
1.9500e+06	14796	14822	26.34	0.27
2.0000e+06	15141	15168	26.67	0.27
2.1000e+06	15835	15856	21.02	0.21
2.2000e+06	16515	16541	26.42	0.26
2.3000e+06	17211	17224	13.02	0.13
2.4000e+06	17922	17904	-18.04	-0.17
2.5000e+06	18604	18581	-22.64	-0.21
2.6000e+06	19283	19256	-26.67	-0.24
2.7000e+06	19933	19929	-4.03	-0.04
2.8000e+06	20602	20599	-2.61	-0.02
2.9000e+06	21283	21268	-15.34	-0.13
3.0000e+06	21934	21934	-0.13	-0.00
3.1000e+06	22606	22598	-7.89	-0.07
3.2000e+06	23272	23260	-11.57	-0.10
3.3000e+06	23906	23921	14.90	0.12
3.4000e+06	24557	24580	22.60	0.18
3.5000e+06	25205	25237	31.56	0.25
3.6000e+06	25865	25892	26.86	0.21
3.7000e+06	26503	26546	42.54	0.33
3.8000e+06	27131	27198	66.65	0.52
3.9000e+06	27789	27848	59.23	0.46
4.0000e+06	28456	28497	41.34	0.31
4.1000e+06	29077	29145	68.00	0.51
4.2000e+06	29746	29791	45.27	0.34
4.3000e+06	30374	30436	62.17	0.46
4.4000e+06	31041	31080	38.74	0.28
4.5000e+06	31679	31722	43.02	0.31
4.6000e+06	32321	32363	42.03	0.30
4.7000e+06	32964	33003	38.82	0.28
4.8000e+06	33611	33641	30.40	0.21
4.9000e+06	34238	34279	40.80	0.28
5.0000e+06	34888	34915	27.06	0.19
5.2000e+06	36151	36184	33.23	0.23
5.4000e+06	37446	37449	3.10	0.02
5.6000e+06	38702	38710	7.85	0.05
5.8000e+06	39945	39967	21.63	0.14
6.0000e+06	41208	41220	11.61	0.07
6.2000e+06	42451	42469	17.93	0.11
6.4000e+06	43705	43715	9.70	0.06
6.6000e+06	44980	44957	-22.93	-0.14
6.8000e+06	46238	46196	-41.86	-0.25
7.0000e+06	47488	47432	-55.98	-0.33
7.2000e+06	48731	48665	-66.19	-0.39
7.4000e+06	49960	49895	-65.40	-0.38
7.6000e+06	51096	51121	25.50	0.15
7.8000e+06	52331	52346	14.58	0.08
8.0000e+06	53583	53567	-16.08	-0.09
8.2000e+06	54778	54786	7.60	0.04
8.4000e+06	56032	56002	-30.31	-0.17
8.6000e+06	57231	57215	-15.74	-0.09
8.8000e+06	58442	58426	-15.63	-0.08
9.0000e+06	59660	59635	-24.90	-0.13
9.2000e+06	60817	60841	24.49	0.13
9.4000e+06	62003	62046	42.60	0.22
9.6000e+06	63207	63247	40.49	0.21
9.8000e+06	64375	64447	72.20	0.37
1.0000e+07	65513	65645	131.80	0.67
1.0500e+07	68511	68630	118.80	0.59
1.1000e+07	71550	71603	52.51	0.26
1.1500e+07	74482	74564	81.56	0.39
1.2000e+07	77477	77514	36.51	0.17
1.2500e+07	80495	80453	-42.14	-0.19
1.3000e+07	83429	83382	-46.90	-0.21
1.3500e+07	86394	86302	-92.35	-0.41
1.4000e+07	89226	89212	-14.08	-0.06
1.4500e+07	92149	92113	-35.72	-0.15
1.5000e+07	95026	95006	-19.95	-0.09
1.5500e+07	97920	97891	-29.43	-0.12
1.6000e+07	100801	100767	-33.87	-0.14
1.6500e+07	103621	103636	15.01	0.06
1.7000e+07	106529	106497	-31.54	-0.13
1.7500e+07	109331	109352	20.74	0.08
1.8000e+07	112150	112199	49.05	0.19
1.8500e+07	115007	115040	32.63	0.13
1.9000e+07	117775	117874	98.68	0.38
1.9500e+07	120591	120701	110.38	0.42
2.0000e+07	123410	123523	112.92	0.42
2.1000e+07	129031	129148	117.18	0.43
2.2000e+07	134669	134751	81.74	0.29
2.3000e+07	140222	140332	109.74	0.39
2.4000e+07	145748	145892	144.22	0.50
2.5000e+07	151327	151433	106.14	0.36
2.6000e+07	156900	156955	55.37	0.19
2.7000e+07	162456	162460	3.70	0.01
2.8000e+07	167969	167947	-22.13	-0.07
2.9000e+07	173425	173418	-7.43	-0.02
3.0000e+07	178927	178872	-54.58	-0.17
3.1000e+07	184427	184312	-114.99	-0.36
3.2000e+07	189827	189737	-90.10	-0.28
3.3000e+07	195220	195148	-72.41	-0.22
3.4000e+07	200651	200545	-106.45	-0.32
3.5000e+07	206051	205928	-122.75	-0.36
3.6000e+07	211411	211299	-111.90	-0.32
3.7000e+07	216821	216657	-163.50	-0.47
3.8000e+07	222156	222004	-152.19	-0.43
3.9000e+07	227538	227338	-199.59	-0.56
4.0000e+07	232763	232662	-101.39	-0.28
4.1000e+07	238121	237974	-147.26	-0.40
4.2000e+07	243347	243275	-71.90	-0.19
4.3000e+07	248618	248566	-52.03	-0.14
4.4000e+07	253843	253847	3.63	0.01
4.5000e+07	259138	259117	-20.67	-0.05
4.6000e+07	264545	264378	-166.69	-0.43
4.7000e+07	269812	269630	-182.18	-0.47
4.8000e+07	275076	274872	-203.92	-0.52
4.9000e+07	280368	280105	-262.71	-0.66
5.0000e+07	285617	285330	-287.32	-0.72
5.2000e+07	296045	295753	-292.27	-0.72
5.4000e+07	306340	306143	-197.30	-0.48
5.6000e+07	316776	316501	-275.05	-0.66
5.8000e+07	326963	326829	-134.25	-0.32
6.0000e+07	337223	337127	-95.74	-0.22
6.2000e+07	347640	347398	-242.44	-0.55
6.4000e+07	357814	357641	-173.33	-0.39
6.6000e+07	368119	367858	-261.46	-0.58
6.8000e+07	378223	378049	-173.97	-0.38
7.0000e+07	388370	388216	-154.01	-0.33
7.2000e+07	398559	398359	-199.80	-0.43
7.4000e+07	408650	408479	-170.62	-0.36
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4.0000e+11	1167819334	1167834369	15035.04	0.64
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4.4000e+11	1276719633	1276730519	10886.37	0.44
4.5000e+11	1303846908	1303855674	8766.19	0.35
4.6000e+11	1330931208	1330943215	12006.59	0.48
4.7000e+11	1357977075	1357994032	16957.21	0.66
4.8000e+11	1384992462	1385008979	16517.05	0.64
4.9000e+11	1411969241	1411988870	19628.95	0.75
5.0000e+11	1438912076	1438934485	22408.96	0.85
5.2000e+11	1492698901	1492725846	26945.42	1.01
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5.6000e+11	1599899765	1599928190	28424.82	1.03
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6.2000e+11	1759820717	1759852991	32274.39	1.11
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6.8000e+11	1918784609	1918821596	36986.53	1.22
7.0000e+11	1971574958	1971615013	40055.44	1.31
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1.0000e+12	2753597777	2753698142	100365.12	2.77
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