Prime p₀= 976878079188895151 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 40 2 28 2 106 2 52 2 46 2 (?)
a_n: 0 2 6 8 48 50 78 80 186 188 240 242 288 290
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: 290
Found by: Spectrum
db: batch=76, k=14, 4 40 28 106 52 46

SPT(16)	976877453431666009	0 34 72 90 132 144 150 172 240 262 268 280 322 340 378 412	-625757229142
SPT(16)	976877494175977573	0 4 28 48 54 58 76 106 138 168 186 190 196 216 240 244	-585012917578
SPT(16)	976877555673084391	0 16 78 96 100 118 120 198 208 286 288 306 310 328 390 406	-523515810760
SPT(16)	976877605781287633	0 64 66 76 78 120 168 180 304 316 364 406 408 418 420 484	-473407607518
STPT(10)	976877893713381659	0 2 18 20 30 32 42 44 60 62	-185475513492
STPT(10)	976877913987406601	0 2 30 32 78 80 126 128 156 158	-165201488550
SPT(16)	976878186448834321	0 22 42 46 100 112 138 198 220 280 306 318 372 376 396 418	107259939170
STPT(10)	976878238766568179	0 2 18 20 30 32 42 44 60 62	159577673028
SPT(16)	976878258137243479	0 12 30 42 52 84 90 132 142 184 190 222 232 244 262 274	178948348328
STPT(10)	976878361178227601	0 2 30 32 60 62 90 92 120 122	281989332450
SPT(16)	976878387688508597	0 50 62 66 80 96 152 162 164 174 230 246 260 264 276 326	308499613446