Prime p₀= 2556463349483865401 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 94 2 22 2 34 2 52 2 106 2 (?)
a_n: 0 2 30 32 126 128 150 152 186 188 240 242 348 350
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: 350
Found by: Penguin
db: batch=82, k=14, 28 94 22 34 52 106

STPT(10)	2556461366842868909	0 2 48 50 90 92 132 134 180 182	-1982640996492
SPT(16)	2556461375678716307	0 86 114 126 174 180 182 200 336 354 356 362 410 422 450 536	-1973805149094
STPT(10)	2556461396546086031	0 2 36 38 78 80 120 122 156 158	-1952937779370
SPT(16)	2556461719300404731	0 36 90 92 98 102 182 212 216 246 326 330 336 338 392 428	-1630183460670
SPT(16)	2556461819857048799	0 62 72 104 108 114 138 168 194 224 248 254 258 290 300 362	-1529626816602
SPT(16)	2556463086740945827	0 16 42 54 76 82 100 112 144 156 174 180 202 214 240 256	-262742919574
STPT(10)	2556463419264935231	0 2 6 8 18 20 30 32 36 38	69781069830
SPT(16)	2556463612248509099	0 8 14 68 80 90 108 120 152 164 182 192 204 258 264 272	262764643698
SPT(16)	2556463723308083467	0 30 84 154 214 216 282 292 414 424 490 492 552 622 676 706	373824218066
STPT(10)	2556463919732007581	0 2 6 8 18 20 30 32 36 38	570248142180
SPT(16)	2556463992758860609	0 18 22 24 40 42 60 88 144 172 190 192 208 210 214 232	643274995208