Prime p₀= 561758991714230207 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 10 2 40 2 16 2 16 2 (?)
a_n: 0 2 30 32 42 44 84 86 102 104 120 122
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: 122
Found by: Rantanplan
db: batch=71, k=12, 28 10 40 16 16

SPT(14)	561758951385369571	0 16 40 52 66 130 150 172 192 256 270 282 306 322	-40328860636
TPT(12)	561758965312718207	0 2 24 26 84 86 102 104 144 146 150 152	-26401512000
TPT(12)	561758972588908691	0 2 18 20 48 50 78 80 210 212 216 218	-19125321516
SPT(14)	561758976109657621	0 36 66 72 78 102 148 150 196 220 226 232 262 298	-15604572586
SPT(14)	561758976341439367	0 12 30 106 126 142 232 324 414 430 450 526 544 556	-15372790840
SPT(14)	561758989425758009	0 8 12 32 68 78 90 140 152 162 198 218 222 230	-2288472198
SPT(14)	561758994205312531	0 42 96 106 112 132 160 168 196 216 222 232 286 328	2491082324
SPT(14)	561759009522779567	0 20 32 56 162 176 204 212 240 254 360 384 396 416	17808549360
SPT(14)	561759019854998737	0 52 70 100 102 156 186 226 256 310 312 342 360 412	28140768530
SPT(14)	561759021571647701	0 6 68 102 126 152 168 230 246 272 296 330 392 398	29857417494
TPT(12)	561759066883502471	0 2 90 92 96 98 156 158 168 170 306 308	75169272264