Prime p₀= 2415623174864355221 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 34 2 58 2 40 2 190 2 28 2 28 2 (?)
a_n: 0 2 36 38 96 98 138 140 330 332 360 362 390 392
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 392
Found by: JayPi
db: batch=82, k=14, 34 58 40 190 28 28

STPT(10)	2415622185449946227	0 2 30 32 42 44 54 56 84 86	-989414408994
SPT(16)	2415622466185488697	0 36 40 64 76 102 106 112 174 180 184 210 222 246 250 286	-708678866524
SPT(16)	2415622668817826177	0 20 26 30 36 56 80 120 140 180 204 224 230 234 240 260	-506046529044
STPT(10)	2415622784273632247	0 2 30 32 72 74 114 116 144 146	-390590722974
STPT(10)	2415622829128991087	0 2 60 62 72 74 84 86 144 146	-345735364134
STPT(10)	2415622980952372811	0 2 6 8 48 50 90 92 96 98	-193911982410
STPT(10)	2415623232318225869	0 2 30 32 60 62 90 92 120 122	57453870648
SPT(16)	2415623473658067307	0 4 42 64 76 90 120 180 286 346 376 390 402 424 462 466	298793712086
STPT(10)	2415623550726375947	0 2 12 14 42 44 72 74 84 86	375862020726
STPT(10)	2415624001639808591	0 2 30 32 78 80 126 128 156 158	826775453370
SPT(16)	2415624103541954677	0 22 36 42 52 60 64 72 94 102 106 114 124 130 144 166	928677599456