Prime p₀= 2777830756939069631 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 28 2 178 2 16 2 82 2 124 2 (?)
a_n: 0 2 18 20 48 50 228 230 246 248 330 332 456 458
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: 458
Found by: JayPi
db: batch=82, k=14, 16 28 178 16 82 124

SPT(16)	2777829755810058239	0 20 42 50 72 78 104 108 314 318 344 350 372 380 402 422	-1001129011392
SPT(16)	2777829900335066573	0 96 126 128 146 168 170 210 266 306 308 330 348 350 380 476	-856604003058
SPT(16)	2777830400911624831	0 40 78 138 156 168 178 246 310 378 388 400 418 478 516 556	-356027444800
SPT(16)	2777830408452058381	0 28 66 90 118 136 148 190 198 240 252 270 298 322 360 388	-348487011250
STPT(10)	2777830484075863421	0 2 6 8 18 20 30 32 36 38	-272863206210
SPT(16)	2777830663519858339	0 54 60 70 84 120 138 144 148 154 172 208 222 232 238 292	-93419211292
STPT(10)	2777830850771379551	0 2 36 38 78 80 120 122 156 158	93832309920
STPT(10)	2777830878968722019	0 2 18 20 60 62 102 104 120 122	122029652388
STPT(10)	2777830925930230127	0 2 42 44 72 74 102 104 144 146	168991160496
STPT(12)	2777831479445801321	0 2 30 32 90 92 180 182 240 242 270 272	722506731690
TPT(14)	2777831595786857417	0 2 54 56 150 152 174 176 192 194 222 224 300 302	838847787786