Prime p₀= 2364036669538551977 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 28 2 10 2 10 2 16 2 130 2 (?)
a_n: 0 2 60 62 90 92 102 104 114 116 132 134 264 266
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: 266
Found by: Xenon
db: batch=81, k=14, 58 28 10 10 16 130

SPT(16)	2364035709941979613	0 16 30 60 88 96 114 154 210 250 268 276 304 334 348 364	-959596572364
STPT(10)	2364035793343787711	0 2 30 32 78 80 126 128 156 158	-876194764266
SPT(13)	2364036374515477097	0 30 36 72 102 120 186 252 270 300 336 342 372	-295023074880
SPT(16)	2364036421542708083	0 30 44 56 68 108 114 134 240 260 266 306 318 330 344 374	-247995843894
SPT(16)	2364036617329070161	0 76 78 102 106 130 142 168 220 246 258 282 286 310 312 388	-52209481816
SPT(16)	2364036628465999829	0 2 14 18 30 42 68 90 122 144 170 182 194 198 210 212	-41072552148
STPT(10)	2364036770421726311	0 2 6 8 18 20 30 32 36 38	100883174334
SPT(20)	2364036770622495011	0 8 26 38 92 96 120 140 156 228 260 332 348 368 392 396 450 462 480 488	101083943034
SPT(16)	2364036900200842717	0 16 36 82 96 112 142 190 222 270 300 316 330 376 396 412	230662290740
TPT(14)	2364037190495159831	0 2 78 80 120 122 156 158 198 200 246 248 276 278	520956607854
SPT(16)	2364037655730378533	0 26 38 68 90 104 168 170 174 176 240 254 276 306 318 344	986191826556