Prime p₀= 2121715713647902079 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 46 2 40 2 16 2 28 2 10 2 (?)
a_n: 0 2 30 32 78 80 120 122 138 140 168 170 180 182
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: 182
Found by: Time_Traveler
db: batch=80, k=14, 28 46 40 16 28 10

SPT(16)	2121714315484278079	0 4 70 102 112 118 144 148 174 178 204 210 220 252 318 322	-1398163624000
STPT(10)	2121714512639595647	0 2 42 44 72 74 102 104 144 146	-1201008306432
SPT(16)	2121714512935252493	0 20 30 38 48 66 108 114 140 146 188 206 216 224 234 254	-1200712649586
SPT(16)	2121714552875385257	0 12 26 62 66 114 126 144 152 170 182 230 234 270 284 296	-1160772516822
SPT(16)	2121715212644425903	0 18 94 120 124 280 354 390 448 484 558 714 718 744 820 838	-501003476176
SPT(16)	2121715508639351453	0 20 48 54 78 90 114 164 180 230 254 266 290 296 324 344	-205008550626
SPT(16)	2121716060513922989	0 8 120 134 138 152 158 180 182 204 210 224 228 242 354 362	346866020910
SPT(16)	2121716087438952583	0 28 40 66 88 94 144 150 154 160 210 216 238 264 276 304	373791050504
STPT(10)	2121716108862338531	0 2 6 8 48 50 90 92 96 98	395214436452
STPT(10)	2121716560390077071	0 2 36 38 78 80 120 122 156 158	846742174992
SPT(16)	2121716612422296311	0 60 78 120 122 162 168 182 186 200 206 246 248 290 308 368	898774394232