Prime p₀= 1124942113068640199 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 130 2 76 2 10 2 76 2 76 2 58 2 (?)
a_n: 0 2 132 134 210 212 222 224 300 302 378 380 438 440
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: 440
Found by: Theadalus
db: batch=76, k=14, 130 76 10 76 76 58

SPT(16)	1124941621848854429	0 72 98 132 170 188 230 258 302 330 372 390 428 462 488 560	-491219785770
STPT(10)	1124941709698846937	0 2 60 62 102 104 144 146 204 206	-403369793262
SPT(16)	1124941841886765223	0 24 48 54 76 90 114 166 168 220 244 258 280 286 310 334	-271181874976
TPT(14)	1124941873062041891	0 2 108 110 258 260 288 290 336 338 390 392 426 428	-240006598308
SPT(16)	1124941877191820473	0 18 24 90 144 148 154 178 186 210 216 220 274 340 346 364	-235876819726
SPT(16)	1124942040065731633	0 48 64 106 120 126 154 166 168 180 208 214 228 270 286 334	-73002908566
STPT(10)	1124942678612905961	0 2 6 8 48 50 90 92 96 98	565544265762
SPT(16)	1124942752655215099	0 22 40 42 64 72 78 88 114 124 130 138 160 162 180 202	639586574900
STPT(10)	1124942789726654531	0 2 6 8 48 50 90 92 96 98	676658014332
SPT(16)	1124942793863606089	0 4 78 82 84 124 138 142 210 214 228 268 270 274 348 352	680794965890
STPT(10)	1124942970409764041	0 2 6 8 48 50 90 92 96 98	857341123842