Prime p₀= 1268616017682281159 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 64 2 10 2 16 2 22 2 34 2 (?)
a_n: 0 2 12 14 78 80 90 92 108 110 132 134 168 170
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: 170
Found by: Megacruncher
db: batch=77, k=14, 10 64 10 16 22 34

SPT(16)	1268614294531669609	0 10 34 54 84 112 174 324 388 538 600 628 658 678 702 712	-1723150611550
SPT(16)	1268615583607906099	0 4 30 40 48 54 70 142 210 282 298 304 312 322 348 352	-434074375060
STPT(10)	1268615606224311647	0 2 30 32 42 44 54 56 84 86	-411457969512
STPT(10)	1268615651669909831	0 2 36 38 78 80 120 122 156 158	-366012371328
TPT(14)	1268615723169546989	0 2 18 20 30 32 72 74 108 110 150 152 228 230	-294512734170
TPT(16)	1268615855070297659	0 2 78 80 132 134 162 164 210 212 228 230 300 302 312 314	-162611983500
STPT(10)	1268616479047444127	0 2 30 32 42 44 54 56 84 86	461365162968
SPT(16)	1268616770692924501	0 16 28 36 70 90 168 198 280 310 388 408 442 450 462 478	753010643342
SPT(16)	1268617100898840947	0 20 60 62 102 104 132 182 192 242 270 272 312 314 354 374	1083216559788
SPT(16)	1268617239930974653	0 16 40 54 100 126 136 144 220 228 238 264 310 324 348 364	1222248693494
SPT(16)	1268617360941565333	0 4 54 66 70 96 108 136 228 256 268 294 298 310 360 364	1343259284174