Prime p₀= 4364296314591379721 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 40 2 10 2 28 2 46 2 70 2 (?)
a_n: 0 2 36 38 78 80 90 92 120 122 168 170 240 242
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: 242
Found by: arkiss
db: batch=85, k=14, 34 40 10 28 46 70

SPT(16)	4364294430145498967	0 26 44 56 60 114 122 126 140 144 152 206 210 222 240 266	-1884445880754
STPT(10)	4364294524640176727	0 2 42 44 72 74 102 104 144 146	-1789951202994
SPT(16)	4364294919501983131	0 18 42 46 108 112 130 136 222 228 246 250 312 316 340 358	-1395089396590
SPT(16)	4364294982255671581	0 6 18 48 60 100 186 238 258 310 396 436 448 478 490 496	-1332335708140
SPT(16)	4364296021286848057	0 52 54 60 82 102 112 154 192 234 244 264 286 292 294 346	-293304531664
SPT(16)	4364296301919983609	0 8 12 20 38 68 78 98 144 164 174 204 222 230 234 242	-12671396112
STPT(12)	4364297279645142899	0 2 12 14 42 44 48 50 78 80 90 92	965053763178
SPT(16)	4364297350013813813	0 38 68 108 168 194 200 206 228 234 240 266 326 366 396 434	1035422434092
SPT(16)	4364297696374898003	0 30 44 50 54 128 156 170 234 248 276 350 354 360 374 404	1381783518282
STPT(10)	4364297795384583767	0 2 12 14 42 44 72 74 84 86	1480793204046
STPT(10)	4364298237628919801	0 2 30 32 78 80 126 128 156 158	1923037540080