Prime p₀= 2377724870919461249 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 40 2 94 2 58 2 40 2 16 2 10 2 (?)
a_n: 0 2 42 44 138 140 198 200 240 242 258 260 270 272
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: 272
Found by: Landjunge
db: batch=81, k=14, 40 94 58 40 16 10

SPT(16)	2377723512951851569	0 18 70 112 114 120 124 142 150 168 172 178 180 222 274 292	-1357967609680
STPT(10)	2377723596224822969	0 2 12 14 30 32 48 50 60 62	-1274694638280
SPT(16)	2377724510448257699	0 2 42 50 84 98 108 120 122 134 144 158 192 200 240 242	-360471203550
STPT(10)	2377724535731359427	0 2 30 32 42 44 54 56 84 86	-335188101822
SPT(16)	2377724591060618167	0 42 60 96 114 124 144 166 330 352 372 382 400 436 454 496	-279858843082
STPT(10)	2377724811657785669	0 2 48 50 60 62 72 74 120 122	-59261675580
SPT(16)	2377725274931454611	0 8 42 50 56 66 72 78 80 86 92 102 108 116 150 158	404011993362
SPT(16)	2377725561362123263	0 16 30 36 70 76 120 148 168 196 240 246 280 286 300 316	690442662014
SPT(13)	2377725672270518497	0 6 30 90 96 120 126 132 156 162 222 246 252	801351057248
SPT(16)	2377725781713067459	0 10 48 72 148 160 190 214 258 282 312 324 400 424 462 472	910793606210
STPT(10)	2377726064977536809	0 2 48 50 90 92 132 134 180 182	1194058075560