Prime p₀= 2027300041396035629 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 10 2 46 2 88 2 16 2 40 2 40 2 (?)
a_n: 0 2 12 14 60 62 150 152 168 170 210 212 252 254
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: 254
Found by: Dingo
db: batch=80, k=14, 10 46 88 16 40 40

SPT(16)	2027298516109207051	0 18 42 72 78 100 106 156 172 222 228 250 256 286 310 328	-1525286828578
SPT(16)	2027298917172276179	0 50 54 80 84 104 120 144 224 248 264 284 288 314 318 368	-1124223759450
SPT(16)	2027298936390897427	0 96 172 220 234 240 312 322 324 334 406 412 426 474 550 646	-1105005138202
TPT(14)	2027299082537968319	0 2 42 44 78 80 168 170 222 224 288 290 372 374	-958858067310
SPT(16)	2027299106065848473	0 24 26 50 66 80 110 134 180 204 234 248 264 288 290 314	-935330187156
STPT(10)	2027299907777095571	0 2 6 8 48 50 90 92 96 98	-133618940058
SPT(16)	2027300121192136261	0 22 28 52 66 72 120 132 136 148 196 202 216 240 246 268	79796100632
STPT(10)	2027300350741108151	0 2 36 38 78 80 120 122 156 158	309345072522
STPT(10)	2027300724907007531	0 2 36 38 78 80 120 122 156 158	683510971902
STPT(10)	2027300999240871587	0 2 72 74 102 104 132 134 204 206	957844835958
TPT(14)	2027301043387766411	0 2 18 20 66 68 180 182 336 338 438 440 480 482	1001991730782