Prime p₀= 1415409121997830901 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 118 2 40 2 88 2 88 2 16 2 (?)
a_n: 0 2 6 8 126 128 168 170 258 260 348 350 366 368
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 368
Found by: Theadalus
db: batch=78, k=14, 4 118 40 88 88 16

SPT(16)	1415407303833278299	0 4 18 78 118 120 124 148 150 174 178 180 220 280 294 298	-1818164552602
SPT(16)	1415408216117192333	0 24 56 60 98 144 170 200 234 264 290 336 374 378 410 434	-905880638568
SPT(16)	1415408234466136987	0 4 10 24 66 70 84 94 102 112 126 130 172 186 192 196	-887531693914
SPT(16)	1415408286786085483	0 24 28 30 108 150 184 190 198 204 238 280 358 360 364 388	-835211745418
STPT(10)	1415408437419384641	0 2 36 38 78 80 120 122 156 158	-684578446260
STPT(10)	1415408736745303877	0 2 90 92 132 134 174 176 264 266	-385252527024
SPT(16)	1415409208318500211	0 36 42 60 70 78 88 102 136 150 160 168 178 196 202 238	86320669310
STPT(10)	1415409328766081027	0 2 30 32 42 44 54 56 84 86	206768250126
TPT(14)	1415409585017805107	0 2 12 14 150 152 162 164 210 212 222 224 264 266	463019974206
SPT(16)	1415409843020240689	0 42 102 108 130 172 220 240 250 270 318 360 382 388 448 490	721022409788
STPT(10)	1415409970237933907	0 2 30 32 42 44 54 56 84 86	848240103006