Prime p₀= 2719716464938212671 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 94 2 22 2 28 2 4 2 22 2 58 2 (?)
a_n: 0 2 96 98 120 122 150 152 156 158 180 182 240 242
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: 242
Found by: [SG-FC] hl
db: batch=82, k=14, 94 22 28 4 22 58

SPT(16)	2719714888547903903	0 26 30 90 98 104 116 126 128 138 150 156 164 224 228 254	-1576390308768
STPT(10)	2719715283939074789	0 2 18 20 30 32 42 44 60 62	-1180999137882
SPT(16)	2719715644481283209	0 42 54 60 90 114 164 180 242 258 308 332 362 368 380 422	-820456929462
STPT(10)	2719716004634232347	0 2 42 44 72 74 102 104 144 146	-460303980324
SPT(18)	2719716068602408801	0 18 28 60 70 90 100 126 148 168 190 216 226 246 256 288 298 316	-396335803870
SPT(16)	2719716090481129139	0 14 24 38 50 72 78 102 140 164 170 192 204 218 228 242	-374457083532
SPT(20)	2719716587596232753	0 8 48 50 90 128 138 140 156 168 188 200 216 218 228 266 306 308 348 356	122658020082
SPT(18)	2719716653680076737	0 12 36 52 70 120 124 126 136 180 190 192 196 246 264 280 304 316	188741864066
STPT(10)	2719716893505939329	0 2 30 32 60 62 90 92 120 122	428567726658
TPT(14)	2719716972355085369	0 2 30 32 42 44 102 104 162 164 210 212 252 254	507416872698
STPT(10)	2719717153739508017	0 2 30 32 42 44 54 56 84 86	688801295346