Prime p₀= 1831363733009628929 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 100 2 46 2 40 2 4 2 70 2 76 2 (?)
a_n: 0 2 102 104 150 152 192 194 198 200 270 272 348 350
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: Paul
db: batch=79, k=14, 100 46 40 4 70 76

SPT(16)	1831362300445649123	0 6 8 50 80 96 126 140 144 158 188 204 234 276 278 284	-1432563979806
TPT(14)	1831362411478400837	0 2 12 14 54 56 114 116 180 182 192 194 240 242	-1321531228092
SPT(16)	1831362551717391859	0 82 108 118 124 132 174 178 234 238 280 288 294 304 330 412	-1181292237070
SPT(16)	1831362874935495767	0 20 42 50 84 90 150 152 162 164 224 230 264 272 294 314	-858074133162
STPT(10)	1831362936257638877	0 2 30 32 60 62 90 92 120 122	-796751990052
STPT(10)	1831363080611392577	0 2 12 14 42 44 72 74 84 86	-652398236352
TPT(14)	1831363781120639021	0 2 18 20 90 92 156 158 168 170 216 218 258 260	48111010092
SPT(16)	1831364009917435447	0 60 72 102 124 130 166 186 220 240 276 282 304 334 346 406	276907806518
STPT(10)	1831364142605822987	0 2 30 32 42 44 54 56 84 86	409596194058
STPT(10)	1831364174260628237	0 2 24 26 42 44 60 62 84 86	441250999308
STPT(10)	1831364249280029081	0 2 36 38 78 80 120 122 156 158	516270400152