Prime p₀= 2796950436498705521 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 58 2 4 2 58 2 10 2 130 2 34 2 (?)
a_n: 0 2 60 62 66 68 126 128 138 140 270 272 306 308
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: 308
Found by: JayPi
db: batch=82, k=14, 58 4 58 10 130 34

SPT(16)	2796949233382850407	0 46 64 66 96 114 142 186 190 234 262 280 310 312 330 376	-1203115855114
STPT(12)	2796949245492572501	0 2 6 8 36 38 210 212 240 242 246 248	-1191006133020
SPT(16)	2796949764475757647	0 30 64 72 82 84 96 106 120 130 142 144 154 162 196 226	-672022947874
STPT(10)	2796949865790090419	0 2 12 14 90 92 168 170 180 182	-570708615102
SPT(16)	2796950167383360361	0 6 16 22 60 66 72 90 172 190 196 202 240 246 256 262	-269115345160
SPT(16)	2796950272611967453	0 10 48 88 108 114 234 238 300 304 424 430 450 490 528 538	-163886738068
SPT(16)	2796950544721246939	0 48 54 72 78 82 88 100 102 114 120 124 130 148 154 202	108222541418
STPT(10)	2796950597711576807	0 2 54 56 72 74 90 92 144 146	161212871286
STPT(10)	2796951219312310829	0 2 18 20 30 32 42 44 60 62	782813605308
SPT(16)	2796951670152243829	0 40 42 112 114 130 142 172 192 222 234 250 252 322 324 364	1233653538308
STPT(10)	2796951812676431819	0 2 12 14 90 92 168 170 180 182	1376177726298