Prime p₀= 14013802405729559 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 28 2 70 2 4 2 28 2 40 2 (?)
a_n: 0 2 30 32 102 104 108 110 138 140 180 182
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: 182
Found by: Farscape
db: batch=62, k=12, 28 70 4 28 40

SPT(14)	14013752601098839	0 12 40 54 64 78 108 154 184 198 208 222 250 262	-49804630720
SPT(14)	14013769465828747	0 10 42 54 70 84 112 114 142 156 172 184 216 226	-32939900812
SPT(14)	14013776022690443	0 20 38 48 86 90 96 98 104 108 146 156 174 194	-26383039116
SPT(16)	14013776938266601	0 16 30 42 46 88 90 100 228 238 240 282 286 298 312 328	-25467462958
SPT(14)	14013780441761311	0 12 18 28 72 102 112 138 148 178 222 232 238 250	-21963968248
SPT(14)	14013797397824881	0 10 30 42 72 96 112 156 172 196 226 238 258 268	-5007904678
SPT(14)	14013853800214711	0 10 18 36 48 70 76 120 126 148 160 178 186 196	51394485152
TPT(12)	14013857503347437	0 2 150 152 180 182 192 194 222 224 294 296	55097617878
SPT(14)	14013878266770197	0 6 60 116 132 134 176 270 312 314 330 386 440 446	75861040638
SPT(14)	14013883769732173	0 10 18 28 84 88 106 108 126 130 186 196 204 214	81364002614
SPT(14)	14013908525869423	0 6 34 36 54 78 118 156 196 220 238 240 268 274	106120139864