Prime p₀= 5541576008690147 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 22 2 4 2 28 2 22 2 28 2 (?)
a_n: 0 2 24 26 30 32 60 62 84 86 114 116
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: 116
Found by: Egon olsen
db: batch=62, k=12, 22 4 28 22 28

SPT(14)	5541562535496737	0 12 32 36 72 80 92 144 156 164 200 204 224 236	-13473193410
SPT(14)	5541564069545069	0 12 14 48 54 60 80 132 152 158 164 198 200 212	-11939145078
SPT(14)	5541564088113791	0 8 26 36 38 50 56 132 138 150 152 162 180 188	-11920576356
SPT(14)	5541573210586487	0 2 26 32 42 90 132 140 182 230 240 246 270 272	-2798103660
TPT(12)	5541573796794479	0 2 90 92 132 134 138 140 162 164 168 170	-2211895668
SPT(14)	5541574707909001	0 28 58 100 108 126 132 136 142 160 168 210 240 268	-1300781146
STPT(10)	5541582261657887	0 2 30 32 42 44 54 56 84 86	6252967740
TPT(12)	5541583912049459	0 2 30 32 42 44 138 140 222 224 240 242	7903359312
TPT(12)	5541585410755439	0 2 48 50 78 80 90 92 180 182 192 194	9402065292
SPT(14)	5541596491005121	0 16 28 30 40 66 70 108 112 138 148 150 162 178	20482314974
SPT(14)	5541596496722773	0 4 18 28 34 60 70 204 214 240 246 256 270 274	20488032626