Prime p₀= 1078214991061022807 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 88 2 34 2 28 2 40 2 10 2 (?)
a_n: 0 2 24 26 114 116 150 152 180 182 222 224 234 236
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: 236
Found by: Daniel
db: batch=76, k=14, 22 88 34 28 40 10

SPT(16)	1078213707786813361	0 12 18 40 70 78 108 192 268 352 382 390 420 442 448 460	-1283274209446
SPT(16)	1078213724615001509	0 8 14 78 90 98 104 120 278 294 300 308 320 384 390 398	-1266446021298
STPT(10)	1078213763785103717	0 2 30 32 72 74 114 116 144 146	-1227275919090
STPT(10)	1078214392039971881	0 2 36 38 78 80 120 122 156 158	-599021050926
STPT(10)	1078214645327586761	0 2 36 38 78 80 120 122 156 158	-345733436046
SPT(20)	1078214677531789921	0 18 22 28 96 102 172 256 270 406 432 568 582 666 736 742 810 816 820 838	-313529232886
SPT(16)	1078215072869374267	0 10 70 102 112 126 142 144 322 324 340 354 364 396 456 466	81808351460
STPT(10)	1078215113431767341	0 2 30 32 60 62 90 92 120 122	122370744534
SPT(16)	1078215709138033397	0 24 26 32 92 126 140 164 222 246 260 294 354 360 362 386	718077010590
SPT(16)	1078215945491575357	0 42 96 132 166 190 244 246 250 252 306 330 364 400 454 496	954430552550
STPT(10)	1078216068147207959	0 2 48 50 90 92 132 134 180 182	1077086185152