Prime p₀= 779403667968021221 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 106 2 28 2 16 2 52 2 136 2 (?)
a_n: 0 2 30 32 138 140 168 170 186 188 240 242 378 380
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: 380
Found by: [SG]FX
db: batch=73, k=14, 28 106 28 16 52 136

SPT(16)	779402466854732339	0 38 62 78 80 90 114 132 170 188 212 222 224 240 264 302	-1201113288882
SPT(16)	779402597726934463	0 10 18 28 76 88 120 150 154 184 216 228 276 286 294 304	-1070241086758
SPT(16)	779402599861384067	0 20 44 62 66 72 84 92 114 122 134 140 144 162 186 206	-1068106637154
SPT(16)	779402633108807233	0 30 36 60 84 138 144 148 186 190 196 250 274 298 304 334	-1034859213988
SPT(16)	779402687782209781	0 16 36 78 96 112 138 160 198 220 246 262 280 322 342 358	-980185811440
SPT(16)	779403153192466841	0 8 20 38 56 96 150 198 230 278 332 372 390 408 420 428	-514775554380
TPT(16)	779404137896095709	0 2 30 32 60 62 252 254 282 284 420 422 468 470 480 482	469928074488
SPT(16)	779405478504968879	0 50 54 158 180 210 260 284 288 312 362 392 414 518 522 572	1810536947658
SPT(16)	779405506681657019	0 8 50 68 84 92 120 134 198 212 240 248 264 282 324 332	1838713635798
SPT(16)	779405556057039841	0 40 48 76 160 166 168 186 202 220 222 228 312 340 348 388	1888089018620
STPT(10)	779406283988178947	0 2 60 62 102 104 144 146 204 206	2616020157726