Prime p₀= 2865134560583959577 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 10 2 40 2 64 2 52 2 34 2 (?)
a_n: 0 2 90 92 102 104 144 146 210 212 264 266 300 302
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: 302
Found by: [SG]ATA-Rolf
db: batch=82, k=14, 88 10 40 64 52 34

STPT(10)	2865132855965223659	0 2 12 14 30 32 48 50 60 62	-1704618735918
STPT(10)	2865133156522245599	0 2 48 50 90 92 132 134 180 182	-1404061713978
STPT(10)	2865133355639891261	0 2 30 32 78 80 126 128 156 158	-1204944068316
SPT(16)	2865133470510800887	0 10 30 40 60 114 172 202 234 264 322 376 396 406 426 436	-1090073158690
STPT(10)	2865133481465158997	0 2 30 32 60 62 90 92 120 122	-1079118800580
SPT(16)	2865134035414444081	0 16 28 52 70 96 198 222 226 250 352 378 396 420 432 448	-525169515496
SPT(16)	2865135275831512399	0 4 24 34 58 72 102 118 144 160 190 204 228 238 258 262	715247552822
STPT(10)	2865135685333495331	0 2 6 8 18 20 30 32 36 38	1124749535754
STPT(10)	2865136197106343261	0 2 6 8 48 50 90 92 96 98	1636522383684
STPT(10)	2865136428376502141	0 2 36 38 78 80 120 122 156 158	1867792542564
STPT(10)	2865136526704817879	0 2 42 44 90 92 138 140 180 182	1966120858302