Prime p₀= 2537872682989877201 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 46 2 40 2 34 2 148 2 22 2 46 2 (?)
a_n: 0 2 48 50 90 92 126 128 276 278 300 302 348 350
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: 350
Found by: [SG-FC] hl
db: batch=82, k=14, 46 40 34 148 22 46

STPT(10)	2537871697195468691	0 2 36 38 78 80 120 122 156 158	-985794408510
SPT(16)	2537871761650991693	0 20 26 36 44 54 78 90 134 146 170 180 188 198 204 224	-921338885508
SPT(16)	2537872051108095179	0 8 14 48 90 98 134 144 164 174 210 218 260 294 300 308	-631881782022
SPT(16)	2537872291946680099	0 24 42 60 78 94 112 118 204 210 228 244 262 280 298 322	-391043197102
SPT(16)	2537872371805370591	0 12 38 62 68 110 122 132 158 168 180 222 228 252 278 290	-311184506610
SPT(16)	2537872537389777061	0 36 40 70 106 112 138 162 166 190 216 222 258 288 292 328	-145600100140
SPT(16)	2537872921873002589	0 24 58 72 84 108 144 154 168 178 214 238 250 264 298 322	238883125388
TPT(14)	2537873003292596861	0 2 6 8 36 38 78 80 126 128 138 140 288 290	320302719660
STPT(10)	2537873211224629319	0 2 18 20 30 32 42 44 60 62	528234752118
SPT(16)	2537873940894938491	0 6 16 28 138 192 198 226 252 280 286 340 450 462 472 478	1257905061290
TPT(14)	2537873970639208079	0 2 60 62 222 224 258 260 270 272 300 302 312 314	1287649330878