Prime p₀= 1041356237477054801 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 76 2 46 2 22 2 4 2 40 2 10 2 (?)
a_n: 0 2 78 80 126 128 150 152 156 158 198 200 210 212
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: 212
Found by: Theadalus
db: batch=76, k=14, 76 46 22 4 40 10

STPT(10)	1041355557518295161	0 2 6 8 18 20 30 32 36 38	-679958759640
STPT(10)	1041355577598687737	0 2 12 14 42 44 72 74 84 86	-659878367064
SPT(18)	1041355946438116741	0 18 60 66 76 78 82 90 148 150 208 216 220 222 232 238 280 298	-291038938060
SPT(16)	1041356031464054717	0 50 54 116 120 204 224 276 344 396 416 500 504 566 570 620	-206013000084
STPT(10)	1041356073978116621	0 2 6 8 48 50 90 92 96 98	-163498938180
SPT(16)	1041356084376603383	0 56 86 110 114 126 134 204 230 300 308 320 324 348 378 434	-153100451418
SPT(16)	1041356310433107859	0 72 82 120 130 142 154 172 180 198 210 222 232 270 280 352	72956053058
SPT(16)	1041356406284287369	0 28 52 58 90 118 132 138 154 160 174 202 234 240 264 292	168807232568
SPT(16)	1041356459886979703	0 24 36 104 126 176 206 216 218 228 258 308 330 398 410 434	222409924902
SPT(16)	1041357137918653429	0 24 34 42 52 90 172 174 178 180 262 300 310 318 328 352	900441598628
SPT(16)	1041357180950855617	0 10 24 30 90 102 120 142 162 184 202 214 274 280 294 304	943473800816