Prime p₀= 2579814527299337507 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 16 2 10 2 64 2 58 2 22 2 (?)
a_n: 0 2 84 86 102 104 114 116 180 182 240 242 264 266
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: JayPi
db: batch=82, k=14, 82 16 10 64 58 22

SPT(18)	2579813802781615537	0 36 42 54 76 96 102 112 142 144 174 184 190 210 232 244 250 286	-724517721970
TPT(14)	2579813850853785881	0 2 60 62 108 110 126 128 168 170 210 212 228 230	-676445551626
STPT(10)	2579813850853785989	0 2 18 20 60 62 102 104 120 122	-676445551518
SPT(16)	2579813874073550551	0 40 42 72 108 120 162 178 180 196 238 250 286 316 318 358	-653225786956
SPT(16)	2579814096097913041	0 28 30 52 72 108 132 178 180 226 250 286 306 328 330 358	-431201424466
SPT(16)	2579814417944699813	0 30 38 194 198 230 258 260 294 296 324 356 360 516 524 554	-109354637694
SPT(16)	2579814548905336661	0 6 20 42 48 86 92 98 150 156 162 200 206 228 242 248	21605999154
STPT(10)	2579814675400213211	0 2 36 38 78 80 120 122 156 158	148100875704
TPT(14)	2579814723760282007	0 2 30 32 42 44 84 86 102 104 114 116 180 182	196460944500
SPT(16)	2579814814797415831	0 28 42 58 100 132 138 160 180 202 208 240 282 298 312 340	287498078324
SPT(16)	2579815116141398089	0 10 28 58 70 78 94 108 160 174 190 198 210 240 258 268	588842060582