Prime p₀= 1257912244563626417 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 148 2 100 2 88 2 16 2 70 2 166 2 (?)
a_n: 0 2 150 152 252 254 342 344 360 362 432 434 600 602
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: 602
Found by: X_FISH
db: batch=77, k=14, 148 100 88 16 70 166

SPT(16)	1257911205830100307	0 24 52 72 106 136 156 160 276 280 300 330 364 384 412 436	-1038733526110
STPT(10)	1257911366910528101	0 2 36 38 78 80 120 122 156 158	-877653098316
SPT(16)	1257911778834055601	0 6 12 42 62 68 120 126 182 188 240 246 266 296 302 308	-465729570816
TPT(14)	1257911998192350041	0 2 6 8 30 32 36 38 90 92 126 128 186 188	-246371276376
SPT(16)	1257912024376884161	0 6 18 26 62 96 120 138 140 158 182 216 252 260 272 278	-220186742256
STPT(10)	1257912105329037017	0 2 30 32 72 74 114 116 144 146	-139234589400
STPT(10)	1257912476956332017	0 2 60 62 72 74 84 86 144 146	232392705600
SPT(16)	1257912605740605883	0 18 34 54 66 136 150 186 238 274 288 358 370 390 406 424	361176979466
STPT(10)	1257912675800187917	0 2 42 44 72 74 102 104 144 146	431236561500
STPT(10)	1257912784411494257	0 2 12 14 72 74 132 134 144 146	539847867840
TPT(14)	1257913051735988057	0 2 42 44 102 104 114 116 174 176 210 212 222 224	807172361640