Prime p₀= 2639564668764941 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 34 2 28 2 40 2 40 2 4 2 (?)
a_n: 0 2 36 38 66 68 108 110 150 152 156 158
All 12 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 158
Found by: crashtech
db: batch=61, k=12, 34 28 40 40 4

SPT(14)	2639549034993697	0 4 10 24 54 60 72 94 106 112 142 156 162 166	-15633771244
SPT(14)	2639551130981293	0 16 18 46 88 90 100 114 124 126 168 196 198 214	-13537783648
SPT(14)	2639551477125007	0 30 34 64 96 106 126 154 174 184 216 246 250 280	-13191639934
SPT(16)	2639551912881553	0 36 70 90 150 168 186 208 216 238 256 274 334 354 388 424	-12755883388
TPT(12)	2639554784841857	0 2 54 56 114 116 180 182 192 194 210 212	-9883923084
SPT(14)	2639557808220071	0 12 26 32 50 62 72 116 126 138 156 162 176 188	-6860544870
SPT(14)	2639571622140433	0 40 94 100 114 120 148 156 184 190 204 210 264 304	6953375492
SPT(14)	2639573467996679	0 2 30 110 120 144 162 260 278 302 312 392 420 422	8799231738
SPT(14)	2639582491003999	0 10 28 114 154 178 184 228 234 258 298 384 402 412	17822239058
STPT(10)	2639592603197351	0 2 6 8 48 50 90 92 96 98	27934432410
SPT(14)	2639597228891683	0 4 30 34 78 90 118 126 154 166 210 214 240 244	32560126742