Prime p₀= 2568370750502651201 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 4 2 118 2 28 2 70 2 10 2 4 2 (?)
a_n: 0 2 6 8 126 128 156 158 228 230 240 242 246 248
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: 248
Found by: JayPi
db: batch=82, k=14, 4 118 28 70 10 4

SPT(16)	2568369822184481881	0 12 30 46 82 118 166 210 298 342 390 426 462 478 496 508	-928318169320
SPT(16)	2568370073705900221	0 6 28 30 70 76 106 118 150 162 192 198 238 240 262 268	-676796750980
STPT(10)	2568370120479229247	0 2 30 32 42 44 54 56 84 86	-630023421954
SPT(16)	2568370239486972469	0 90 120 138 148 154 160 168 280 288 294 300 310 328 358 448	-511015678732
STPT(10)	2568370355836306139	0 2 18 20 30 32 42 44 60 62	-394666345062
STPT(10)	2568370665203111267	0 2 42 44 72 74 102 104 144 146	-85299539934
TPT(14)	2568370770804925739	0 2 30 32 72 74 132 134 168 170 210 212 240 242	20302274538
TPT(14)	2568370946697231341	0 2 30 32 96 98 108 110 150 152 240 242 246 248	196194580140
SPT(16)	2568371212000104611	0 38 42 48 50 60 86 122 126 162 188 198 200 206 210 248	461497453410
STPT(10)	2568371292204154637	0 2 30 32 72 74 114 116 144 146	541701503436
STPT(10)	2568371333288449691	0 2 30 32 60 62 90 92 120 122	582785798490