Prime p₀= 1144671178576689737 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 10 2 76 2 130 2 28 2 88 2 (?)
a_n: 0 2 30 32 42 44 120 122 252 254 282 284 372 374
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: 374
Found by: Putin Has a Small Dick
db: batch=76, k=14, 28 10 76 130 28 88

STPT(10)	1144670088990815111	0 2 6 8 48 50 90 92 96 98	-1089585874626
STPT(10)	1144670601709801391	0 2 36 38 78 80 120 122 156 158	-576866888346
SPT(16)	1144670846558651933	0 14 30 54 56 86 104 164 180 240 258 288 290 314 330 344	-332018037804
TPT(14)	1144670915855918021	0 2 30 32 60 62 138 140 156 158 180 182 270 272	-262720771716
SPT(16)	1144670954546069309	0 30 42 74 102 104 144 150 164 170 210 212 240 272 284 314	-224030620428
STPT(10)	1144671063287578949	0 2 48 50 90 92 132 134 180 182	-115289110788
STPT(10)	1144671231606561479	0 2 42 44 60 62 78 80 120 122	53029871742
SPT(16)	1144671312964840519	0 18 34 40 48 60 84 112 150 178 202 214 222 228 244 262	134388150782
SPT(16)	1144672093662007019	0 44 68 90 98 158 168 174 308 314 324 384 392 414 438 482	915085317282
STPT(10)	1144673198356898261	0 2 6 8 18 20 30 32 36 38	2019780208524
SPT(16)	1144673329899349123	0 4 34 40 58 66 76 84 100 108 118 126 144 150 180 184	2151322659386