Prime p₀= 1122867157334117759 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 88 2 40 2 46 2 16 2 10 2 10 2 (?)
a_n: 0 2 90 92 132 134 180 182 198 200 210 212 222 224
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: 224
Found by: Theadalus
db: batch=76, k=14, 88 40 46 16 10 10

SPT(16)	1122866188540244177	0 30 56 80 120 150 152 162 200 210 212 242 282 306 332 362	-968793873582
STPT(10)	1122866286869088401	0 2 6 8 48 50 90 92 96 98	-870465029358
SPT(16)	1122866685123008627	0 42 54 60 74 86 90 126 230 266 270 282 296 302 314 356	-472211109132
SPT(16)	1122866685465309833	0 6 14 44 54 74 110 126 158 174 210 230 240 270 278 284	-471868807926
STPT(10)	1122866707915848989	0 2 18 20 30 32 42 44 60 62	-449418268770
STPT(10)	1122867001974317651	0 2 6 8 18 20 30 32 36 38	-155359800108
SPT(16)	1122867782309344679	0 12 44 80 108 138 158 188 234 264 284 314 342 378 410 422	624975226920
SPT(16)	1122867789757484893	0 6 16 58 70 78 100 108 118 126 148 156 168 210 220 226	632423367134
STPT(12)	1122867875502567839	0 2 12 14 72 74 78 80 138 140 150 152	718168450080
TPT(14)	1122868333926178517	0 2 42 44 54 56 60 62 150 152 192 194 252 254	1176592060758
STPT(10)	1122868711454422949	0 2 78 80 120 122 162 164 240 242	1554120305190