Prime p₀= 865687147007565851 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 28 2 10 2 70 2 106 2 40 2 (?)
a_n: 0 2 36 38 66 68 78 80 150 152 258 260 300 302
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: 302
Found by: Frank [NT]
db: batch=73, k=14, 34 28 10 70 106 40

SPT(16)	865686135308054143	0 28 88 154 160 168 178 180 208 210 220 228 234 300 360 388	-1011699511708
TPT(14)	865686180172579397	0 2 60 62 132 134 294 296 324 326 462 464 492 494	-966834986454
SPT(16)	865686210522254981	0 6 32 80 90 132 140 146 186 192 200 242 252 300 326 332	-936485310870
STPT(10)	865686262649473019	0 2 18 20 30 32 42 44 60 62	-884358092832
SPT(16)	865686594424709963	0 20 24 66 90 156 240 248 306 314 398 464 488 530 534 554	-552582855888
STPT(10)	865687042161863357	0 2 42 44 72 74 102 104 144 146	-104845702494
SPT(16)	865687255927139047	0 34 72 84 124 162 166 190 216 240 244 282 322 334 372 406	108919573196
STPT(10)	865687355556779027	0 2 30 32 42 44 54 56 84 86	208549213176
STPT(10)	865687651113966389	0 2 42 44 60 62 78 80 120 122	504106400538
SPT(16)	865688016271004057	0 26 42 66 74 96 150 152 174 176 230 252 260 284 300 326	869263438206
SPT(16)	865688471360998931	0 6 48 72 86 92 98 122 126 150 156 162 176 200 242 248	1324353433080