Prime p₀= 2589688594171992629 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 106 2 10 2 100 2 28 2 124 2 22 2 (?)
a_n: 0 2 108 110 120 122 222 224 252 254 378 380 402 404
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: 404
Found by: JayPi
db: batch=82, k=14, 106 10 100 28 124 22

SPT(16)	2589686715849540451	0 6 36 42 48 58 106 118 210 222 270 280 286 292 322 328	-1878322452178
STPT(10)	2589686830184633981	0 2 6 8 48 50 90 92 96 98	-1763987358648
STPT(10)	2589687085446722621	0 2 6 8 48 50 90 92 96 98	-1508725270008
TPT(14)	2589687224011595879	0 2 12 14 78 80 90 92 132 134 150 152 162 164	-1370160396750
SPT(16)	2589687998406587707	0 66 76 90 96 144 160 210 220 270 286 334 340 354 364 430	-595765404922
SPT(18)	2589688289951314511	0 18 120 180 182 212 222 240 260 270 290 308 318 348 350 410 512 530	-304220678118
SPT(16)	2589688786610684917	0 36 42 46 72 96 100 112 174 186 190 214 240 244 250 286	192438692288
STPT(10)	2589689360908545197	0 2 30 32 42 44 54 56 84 86	766736552568
STPT(10)	2589689399749598351	0 2 6 8 18 20 30 32 36 38	805577605722
SPT(16)	2589689480654084167	0 22 52 84 106 126 150 156 190 196 220 240 262 294 324 346	886482091538
STPT(10)	2589689495975971061	0 2 30 32 78 80 126 128 156 158	901803978432