Prime p₀= 2956901782368334679 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 100 2 34 2 100 2 16 2 202 2 4 2 (?)
a_n: 0 2 102 104 138 140 240 242 258 260 462 464 468 470
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: 470
Found by: ginga
db: batch=82, k=14, 100 34 100 16 202 4

SPT(16)	2956899500964679423	0 6 18 58 76 84 88 118 126 156 160 168 186 226 238 244	-2281403655256
STPT(10)	2956899556369528739	0 2 12 14 30 32 48 50 60 62	-2225998805940
TPT(14)	2956899737050907621	0 2 108 110 138 140 150 152 156 158 276 278 288 290	-2045317427058
STPT(10)	2956900031777653187	0 2 30 32 72 74 114 116 144 146	-1750590681492
STPT(12)	2956900552660478447	0 2 72 74 84 86 90 92 102 104 174 176	-1229707856232
SPT(16)	2956901075784675977	0 84 86 96 102 156 192 200 276 284 320 374 380 390 392 476	-706583658702
SPT(16)	2956901785934167567	0 6 40 52 72 126 132 136 216 220 226 280 300 312 346 352	3565832888
TPT(14)	2956902863856671459	0 2 30 32 72 74 78 80 90 92 270 272 288 290	1081488336780
STPT(10)	2956903054001535017	0 2 30 32 42 44 54 56 84 86	1271633200338
SPT(18)	2956903058135113531	0 16 22 30 42 90 96 126 198 250 322 352 358 406 418 426 432 448	1275766778852
STPT(10)	2956903435529232071	0 2 36 38 78 80 120 122 156 158	1653160897392