Prime p₀= 774968312656453829 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 40 2 106 2 40 2 28 2 16 2 (?)
a_n: 0 2 18 20 60 62 168 170 210 212 240 242 258 260
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: 260
Found by: GLeeM
db: batch=73, k=14, 16 40 106 40 28 16

SPT(16)	774966885678242189	0 30 32 50 60 74 164 170 204 210 300 314 324 342 344 374	-1426978211640
SPT(16)	774967316357184971	0 26 48 60 86 122 140 146 192 198 216 252 278 290 312 338	-996299268858
TPT(14)	774967639066968119	0 2 42 44 78 80 120 122 132 134 168 170 192 194	-673589485710
STPT(10)	774967757164867697	0 2 12 14 72 74 132 134 144 146	-555491586132
TPT(14)	774967843991966657	0 2 42 44 102 104 132 134 180 182 264 266 324 326	-468664487172
STPT(10)	774968033086588961	0 2 6 8 48 50 90 92 96 98	-279569864868
SPT(16)	774968347999652491	0 12 18 42 100 102 130 142 168 180 208 210 268 292 298 310	35343198662
STPT(12)	774968548620147221	0 2 18 20 60 62 96 98 138 140 156 158	235963693392
SPT(16)	774968822451467933	0 20 38 50 60 78 90 108 116 134 146 164 174 186 204 224	509795014104
SPT(16)	774968857470055627	0 12 16 54 70 100 124 184 192 252 276 306 322 360 364 376	544813601798
TPT(14)	774968892177794099	0 2 42 44 90 92 102 104 210 212 240 242 258 260	579521340270