Prime p₀= 2362409035765051307 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 70 2 40 2 76 2 76 2 118 2 10 2 (?)
a_n: 0 2 72 74 114 116 192 194 270 272 390 392 402 404
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: 404
Found by: Landjunge
db: batch=81, k=14, 70 40 76 76 118 10

SPT(16)	2362407409975450417	0 4 6 10 34 144 172 250 306 384 412 522 546 550 552 556	-1625789600890
TPT(14)	2362407434474804219	0 2 18 20 138 140 180 182 312 314 348 350 360 362	-1601290247088
STPT(10)	2362407857967413027	0 2 72 74 102 104 132 134 204 206	-1177797638280
SPT(18)	2362407877620785041	0 28 40 42 76 78 82 126 130 168 172 216 220 222 256 258 270 298	-1158144266266
STPT(10)	2362408285134059597	0 2 30 32 42 44 54 56 84 86	-750630991710
SPT(16)	2362408863761191823	0 6 18 84 110 120 128 156 158 186 194 204 230 296 308 314	-172003859484
STPT(10)	2362409303601918479	0 2 18 20 30 32 42 44 60 62	267836867172
SPT(16)	2362409382606917341	0 70 76 88 130 166 168 172 216 220 222 258 300 312 318 388	346841866034
SPT(16)	2362409398518481259	0 44 72 80 114 230 264 278 294 308 342 458 492 500 528 572	362753429952
SPT(16)	2362409592968211361	0 28 42 58 108 142 150 168 172 190 198 232 282 298 312 340	557203160054
SPT(16)	2362409846774489069	0 12 24 54 60 104 122 134 150 162 180 224 230 260 272 284	811009437762