Prime p₀= 2040458004745951559 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 16 2 22 2 184 2 40 2 76 2 40 2 (?)
a_n: 0 2 18 20 42 44 228 230 270 272 348 350 390 392
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: Landjunge
db: batch=80, k=14, 16 22 184 40 76 40

TPT(14)	2040457180905706307	0 2 42 44 54 56 84 86 90 92 120 122 132 134	-823840245252
STPT(12)	2040457180905706349	0 2 12 14 42 44 48 50 78 80 90 92	-823840245210
STPT(10)	2040457523966276081	0 2 6 8 18 20 30 32 36 38	-480779675478
STPT(10)	2040457720198402259	0 2 18 20 30 32 42 44 60 62	-284547549300
STPT(10)	2040457770335576477	0 2 54 56 72 74 90 92 144 146	-234410375082
STPT(10)	2040457832979773717	0 2 42 44 72 74 102 104 144 146	-171766177842
SPT(16)	2040458634295090661	0 42 72 92 98 108 120 158 210 248 260 270 276 296 326 368	629549139102
SPT(16)	2040458717883502369	0 4 10 12 22 24 52 78 94 120 148 150 160 162 168 172	713137550810
SPT(16)	2040458875873946471	0 12 48 56 62 138 140 188 270 318 320 396 402 410 446 458	871127994912
SPT(16)	2040459029155042303	0 66 106 114 124 168 184 208 306 330 346 390 400 408 448 514	1024409090744
SPT(16)	2040459047712348479	0 32 90 102 104 110 144 164 168 188 222 228 230 242 300 332	1042966396920