Prime p₀= 19670984477440577 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 118 2 28 2 100 2 76 2 10 2 (?)
a_n: 0 2 30 32 150 152 180 182 282 284 360 362 372 374
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: 374
Found by: crashtech
db: batch=62, k=14, 28 118 28 100 76 10

SPT(14)	19670956127767513	0 24 70 78 90 126 136 258 268 304 316 324 370 394	-28349673064
SPT(14)	19670966536586221	0 6 30 48 90 108 120 148 160 178 220 238 262 268	-17940854356
SPT(14)	19670971977754333	0 18 70 78 84 88 108 190 210 214 220 228 280 298	-12499686244
TPT(12)	19670973451773899	0 2 48 50 78 80 132 134 138 140 162 164	-11025666678
SPT(14)	19670974627888811	0 42 66 78 80 96 122 126 152 168 170 182 206 248	-9849551766
SPT(14)	19670980754832947	0 2 14 44 56 60 92 144 176 180 192 222 234 236	-3722607630
SPT(14)	19671005335473431	0 8 18 38 60 66 78 80 92 98 120 140 150 158	20858032854
SPT(14)	19671012174619583	0 18 24 30 38 56 66 218 228 246 254 260 266 284	27697179006
SPT(14)	19671015667747637	0 36 50 62 90 96 120 242 266 272 300 312 326 362	31190307060
SPT(14)	19671022840127741	0 90 158 168 186 200 206 252 258 272 290 300 368 458	38362687164
SPT(14)	19671039856439051	0 20 36 38 62 66 90 98 122 126 150 152 168 188	55378998474