Prime p₀= 371368663925566121 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 4 2 40 2 16 2 10 2 58 2 (?)
a_n: 0 2 6 8 48 50 66 68 78 80 138 140
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: 140
Found by: Ralfy
db: batch=70, k=12, 4 40 16 10 58

SPT(14)	371368625687698763	0 20 24 56 98 104 108 116 120 126 168 200 204 224	-38237867358
TPT(12)	371368626098494721	0 2 30 32 138 140 156 158 168 170 186 188	-37827071400
SPT(14)	371368643757199727	0 2 30 42 62 66 90 122 146 150 170 182 210 212	-20168366394
SPT(14)	371368647324322541	0 20 50 56 80 126 180 188 242 288 312 318 348 368	-16601243580
SPT(14)	371368650296310419	0 12 32 44 54 90 114 128 152 188 198 210 230 242	-13629255702
SPT(16)	371368663836874307	0 2 80 86 114 146 164 182 234 252 270 302 330 336 414 416	-88691814
SPT(14)	371368674876542663	0 24 26 80 104 116 140 144 168 180 204 258 260 284	10950976542
SPT(14)	371368697007847901	0 32 38 60 62 90 140 150 200 228 230 252 258 290	33082281780
SPT(14)	371368709742880061	0 2 6 38 72 80 90 98 108 116 150 182 186 188	45817313940
SPT(14)	371368710017616007	0 4 22 54 64 90 112 264 286 312 322 354 372 376	46092049886
TPT(12)	371368718306311511	0 2 78 80 90 92 126 128 156 158 240 242	54380745390