Prime p₀= 7440019521350111 starts a Tuple of 12 consecutive primes, which form 6 twin primes (TPT).
d_n: 0 2 46 2 16 2 10 2 70 2 94 2 (?)
a_n: 0 2 48 50 66 68 78 80 150 152 246 248
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: 248
Found by: crashtech
db: batch=62, k=12, 46 16 10 70 94

TPT(12)	7439975653365509	0 2 18 20 42 44 48 50 72 74 102 104	-43867984602
STPT(10)	7439976059565821	0 2 36 38 78 80 120 122 156 158	-43461784290
SPT(14)	7439981918320687	0 36 114 142 162 180 184 192 196 214 234 262 340 376	-37603029424
SPT(14)	7439992518868207	0 22 46 60 82 106 166 210 270 294 316 330 354 376	-27002481904
SPT(14)	7440007713666289	0 82 88 90 112 114 144 208 238 240 262 264 270 352	-11807683822
SPT(14)	7440008753776453	0 64 96 100 108 148 150 154 156 196 204 208 240 304	-10767573658
TPT(12)	7440021489417089	0 2 18 20 42 44 108 110 198 200 240 242	1968066978
SPT(16)	7440023252965123	0 10 16 28 34 36 78 90 94 106 148 150 156 168 174 184	3731615012
SPT(14)	7440043244610817	0 12 24 84 112 120 130 144 154 162 190 250 262 274	23723260706
SPT(14)	7440045024115747	0 40 64 96 120 124 196 240 312 316 340 372 396 436	25502765636
SPT(14)	7440048152586943	0 28 40 70 76 84 88 126 130 138 144 174 186 214	28631236832