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Old 2019-12-27, 14:53   #3
rudy235
 
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Jun 2015
Vallejo, CA/.

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Quote:
Originally Posted by mart_r View Post
You might want to have a look at this paper, which lists record gaps between prime quadruplets up to 10^15:
https://arxiv.org/abs/1309.4053
Thank you very much. Very interesting read.

Here is a more complete table of First Occurrences. (It is easy to prove GAPS 2 mod 7 and 5 mod 7 do not exist.

There were a couple of mistakes in the previous table This is the corrected version
Note gaps like 2,5,9,12,16,19,23,26,30,33,37,40,44,47,51,54,58,61,65,68,72,75,79,82,86,89,93,96,100… and all 2 mod7 or 5 mod cannot exist.

Code:
GAP    After Quadruple
1	1006301

3	11

4	1246241

6	3512051

7	1871

8	632081

10	1121831

11	15731

13	1481

14	1155611

15	1068251

17	18911

18	284741

20	12390011

21	191

22	821

24	3837131

25	875261

27	854921

28	10865291

29	18041

31	958541

32	680291

34	299471

35	1063961

36	663581

38	165701

39	2081

41    Unknown

42	21011

43	97841

45	79691

46	2223671

48	1022501

49	3436241

50	300491

52	294311

53	19421

55     Unknown

56	81041

57	463451

59	442571

60	419051

62	1902611

63	734471

64	6054281

66	16061

67	6332861

69	10037381

70	2246141

71	266681

73	3461

74	855731

76	67211

77	358901

78	7159511

80	2761721

81	77261

83	661091

84	1006331

85	257861

87	467471

88	13001

90	389561

91	69491

92	116531

94	2846861

95	594821

97	119291

98	1003361

99	11718821

101	22271

102	1230371

104	31721

105	2728541

106	1830341

108	1065011

109	5154761

111	654161

112	833711

113   Unknown

115	1627601

116	1912451

118	9585881

119	9431

120	295871

122	240041

123	5248091

125	22692611

126	5651

127	1023941

129	6880871

130	243701

132	2875331

133	51341

134	1798631

136	8557721

137	1588751

139	5201291

140	559211

141	62981

143	2541941

144	166841

146	397751

147	6556601

148	8827541

150	5234681

151	1122131

153	4575281

154	495611

155	354251

157	741751

158	2418671

160  Unknown

161	768191

162	13179581

164	1616801

165	1954361

167  Unknown

168	72221

169	19842671

171	1324571

172   Unknown

174   Unkown

175	2413421

176	2002331

178	14912741

179	978071

181  Unknown
182	340931
183  Unknown
185	14877671
186   Unknown
188	1791731
189	2136131
190	1508621
192	195731
193	1904471
195	6187451
196	1157831
197 Unknown
199	4734671
200	823721


The largest gap I've found is 5261  after 21872441
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