Prime p₀= 1417028803316955737 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 70 2 46 2 58 2 40 2 10 2 (?)
a_n: 0 2 30 32 102 104 150 152 210 212 252 254 264 266
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: UBT - Timbo
db: batch=78, k=14, 28 70 46 58 40 10

STPT(10)	1417026846804204479	0 2 18 20 30 32 42 44 60 62	-1956512751258
SPT(16)	1417027116719589967	0 34 70 96 100 106 120 126 154 160 174 180 184 210 246 280	-1686597365770
TPT(14)	1417027278678393791	0 2 36 38 66 68 78 80 120 122 168 170 210 212	-1524638561946
TPT(16)	1417027919129589521	0 2 138 140 240 242 306 308 396 398 408 410 438 440 516 518	-884187366216
SPT(16)	1417027965826598009	0 2 30 84 132 152 162 170 222 230 240 260 308 362 390 392	-837490357728
SPT(16)	1417028008229841677	0 20 42 80 102 120 146 186 206 246 272 290 312 350 372 392	-795087114060
SPT(16)	1417028994978542369	0 62 74 102 110 188 224 284 288 348 384 462 470 498 510 572	191661586632
SPT(16)	1417029182952816533	0 6 8 14 48 66 114 126 128 140 188 206 240 246 248 254	379635860796
SPT(16)	1417029290939126573	0 18 38 56 86 126 156 206 210 260 290 330 360 378 398 416	487622170836
SPT(16)	1417029586782385729	0 30 52 88 90 112 114 168 184 238 240 262 264 300 322 352	783465429992
SPT(20)	1417029932835667529	0 54 120 134 162 222 228 264 344 348 374 378 458 494 500 560 588 602 668 722	1129518711792