Prime p₀= 1459863306446810537 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 82 2 28 2 34 2 28 2 58 2 10 2 (?)
a_n: 0 2 84 86 114 116 150 152 180 182 240 242 252 254
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: 254
Found by: Spectrum
db: batch=78, k=14, 82 28 34 28 58 10

SPT(16)	1459861177404944957	0 2 14 32 42 56 62 66 80 84 90 104 114 132 144 146	-2129041865580
STPT(10)	1459862164140569219	0 2 30 32 60 62 90 92 120 122	-1142306241318
SPT(13)	1459862229193630013	0 30 78 90 114 174 204 234 294 318 330 378 408	-1077253180524
SPT(16)	1459862556208391947	0 42 82 84 94 100 124 150 166 192 216 222 232 234 274 316	-750238418590
SPT(16)	1459862764500766667	0 12 20 32 74 84 116 152 174 210 242 252 294 306 314 326	-541946043870
SPT(16)	1459863217394630039	0 8 14 60 68 92 140 180 182 222 270 294 302 348 354 362	-89052180498
SPT(16)	1459863583718597171	0 30 38 78 80 98 126 140 228 242 270 288 290 330 338 368	277271786634
SPT(16)	1459863587741741911	0 58 102 106 150 178 252 282 436 466 540 568 612 616 660 718	281294931374
TPT(14)	1459863766915990517	0 2 12 14 132 134 144 146 174 176 210 212 222 224	460469179980
SPT(16)	1459863907591782461	0 38 66 86 108 116 138 140 168 170 192 200 222 242 270 308	601144971924
STPT(10)	1459864164292504379	0 2 12 14 90 92 168 170 180 182	857845693842