Prime p₀= 1089218052839898827 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 28 2 28 2 22 2 136 2 10 2 28 2 (?)
a_n: 0 2 30 32 60 62 84 86 222 224 234 236 264 266
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: 266
Found by: [SG]ATA-Rolf
db: batch=76, k=14, 28 28 22 136 10 28

SPT(16)	1089216086319973021	0 42 60 82 138 172 190 222 238 270 288 322 378 400 418 460	-1966519925806
SPT(16)	1089216236989758029	0 14 60 102 120 122 132 140 144 152 162 164 182 224 270 284	-1815850140798
SPT(16)	1089216594353438389	0 42 60 88 90 94 112 130 132 150 168 172 174 202 220 262	-1458486460438
SPT(16)	1089217511123678653	0 28 30 40 54 84 138 148 156 166 220 250 264 274 276 304	-541716220174
SPT(16)	1089217617628633579	0 4 28 30 52 64 102 130 132 160 198 210 232 234 258 262	-435211265248
STPT(10)	1089217824523969961	0 2 6 8 18 20 30 32 36 38	-228315928866
SPT(16)	1089218220942972893	0 38 54 68 138 164 174 266 288 380 390 416 486 500 516 554	168103074066
SPT(16)	1089218239343455957	0 54 64 106 120 136 172 186 400 414 450 466 480 522 532 586	186503557130
SPT(16)	1089218340908136073	0 6 46 130 166 186 228 258 298 328 370 390 426 510 550 556	288068237246
SPT(16)	1089218705763121057	0 10 12 42 54 70 82 174 280 372 384 400 412 442 444 454	652923222230
SPT(16)	1089218744326961329	0 22 30 54 58 132 138 160 252 274 280 354 358 382 390 412	691487062502