Господа!
Вы можете проверить для следующих чётных длин кортежей.
Вот выписала теоретические паттерны для длин 32 - 50

a(32)
0 6 8 12 18 20 26 32 36 38 42 48 50 56 60 78 80 98 102 108 110 116 120 122 126 132 138 140 146 150 152 158
0 6 8 12 18 20 26 36 38 42 48 50 56 60 62 78 80 96 98 102 108 110 116 120 122 132 138 140 146 150 152 158
a(34)
0 4 10 12 16 22 24 30 36 40 42 46 52 54 60 64 82 84 102 106 112 114 120 124 126 130 136 142 144 150 154 156 162 166
0 4 10 12 16 22 24 30 40 42 46 52 54 60 64 66 82 84 100 102 106 112 114 120 124 126 136 142 144 150 154 156 162 166
a(36)
0 6 10 16 18 22 28 30 36 42 46 48 52 58 60 66 70 88 90 108 112 118 120 126 130 132 136 142 148 150 156 160 162 168 172 178
a(38)
0 8 14 18 24 26 30 36 38 44 50 54 56 60 66 68 74 78 96 98 116 120 126 128 134 138 140 144 150 156 158 164 168 170 176 180 186 194
a(40)
0 4 12 18 22 28 30 34 40 42 48 54 58 60 64 70 72 78 82 100 102 120 124 130 132 138 142 144 148 154 160 162 168 172 174 180 184 190 198 202
a(42)
0 6 10 18 24 28 34 36 40 46 48 54 60 64 66 70 76 78 84 88 106 108 126 130 136 138 144 148 150 154 160 166 168 174 178 180 186 190 196 204 208 214
a(44)
0 4 6 10 12 16 24 30 34 40 42 46 52 54 60 66 70 72 76 82 84 112 114 142 144 150 154 156 160 166 172 174 180 184 186 192 196 202 210 214 216 220 222 226
0 4 6 10 12 16 24 30 34 40 42 46 52 54 66 70 72 76 82 84 90 112 114 136 142 144 150 154 156 160 172 174 180 184 186 192 196 202 210 214 216 220 222 226
0 4 6 10 12 16 24 34 40 42 46 52 54 66 70 72 76 82 84 90 96 112 114 130 136 142 144 150 154 156 160 172 174 180 184 186 192 202 210 214 216 220 222 226
0 4 6 12 16 24 30 34 40 42 46 52 54 60 66 70 72 76 82 84 94 112 114 132 142 144 150 154 156 160 166 172 174 180 184 186 192 196 202 210 214 220 222 226
0 4 6 12 16 24 30 34 40 42 46 52 54 60 66 70 72 76 82 90 94 112 114 132 136 144 150 154 156 160 166 172 174 180 184 186 192 196 202 210 214 220 222 226
0 4 6 12 16 24 30 34 40 42 46 52 54 60 66 70 76 82 84 90 94 112 114 132 136 142 144 150 156 160 166 172 174 180 184 186 192 196 202 210 214 220 222 226
0 4 6 12 16 24 30 34 40 42 46 52 54 60 70 72 76 82 84 90 94 112 114 132 136 142 144 150 154 156 166 172 174 180 184 186 192 196 202 210 214 220 222 226
0 4 6 12 16 24 30 34 40 42 46 52 54 66 70 72 76 82 84 90 94 112 114 132 136 142 144 150 154 156 160 172 174 180 184 186 192 196 202 210 214 220 222 226
0 4 6 12 16 24 30 34 40 46 52 54 60 66 70 72 76 82 84 90 94 112 114 132 136 142 144 150 154 156 160 166 172 174 180 186 192 196 202 210 214 220 222 226
0 4 6 12 16 24 34 40 42 46 52 54 60 66 70 72 76 82 84 90 94 112 114 132 136 142 144 150 154 156 160 166 172 174 180 184 186 192 202 210 214 220 222 226
0 4 6 12 16 30 34 40 42 46 52 54 60 70 72 76 82 84 90 94 96 112 114 130 132 136 142 144 150 154 156 166 172 174 180 184 186 192 196 210 214 220 222 226
0 6 12 16 24 30 34 40 42 46 52 54 60 66 70 72 76 82 84 90 94 112 114 132 136 142 144 150 154 156 160 166 172 174 180 184 186 192 196 202 210 214 220 226
a(46)
0 14 18 20 24 26 30 38 44 48 54 56 60 66 68 74 80 84 86 90 96 98 126 128 156 158 164 168 170 174 180 186 188 194 198 200 206 210 216 224 228 230 234 236 240 254
0 14 18 20 24 26 30 38 44 48 54 56 60 66 68 80 84 86 90 96 98 104 126 128 150 156 158 164 168 170 174 186 188 194 198 200 206 210 216 224 228 230 234 236 240 254
0 14 18 20 24 26 30 38 48 54 56 60 66 68 80 84 86 90 96 98 104 110 126 128 144 150 156 158 164 168 170 174 186 188 194 198 200 206 216 224 228 230 234 236 240 254
0 14 18 20 26 30 38 44 48 54 56 60 66 68 74 80 84 86 90 96 98 108 126 128 146 156 158 164 168 170 174 180 186 188 194 198 200 206 210 216 224 228 234 236 240 254
0 14 18 20 26 30 38 44 48 54 56 60 66 68 80 84 86 90 96 98 104 108 126 128 146 150 156 158 164 168 170 174 186 188 194 198 200 206 210 216 224 228 234 236 240 254
a(48)
0 4 18 22 24 28 30 34 42 48 52 58 60 64 70 72 78 84 88 90 94 100 102 130 132 160 162 168 172 174 178 184 190 192 198 202 204 210 214 220 228 232 234 238 240 244 258 262
0 4 18 22 24 30 34 42 48 52 58 60 64 70 72 78 84 88 90 94 100 102 112 130 132 150 160 162 168 172 174 178 184 190 192 198 202 204 210 214 220 228 232 238 240 244 258 262
a(50)
0 2 8 12 26 30 32 36 38 42 50 56 60 66 68 72 78 80 86 92 96 98 102 108 138 140 170 176 180 182 186 192 198 200 206 210 212 218 222 228 236 240 242 246 248 252 266 270 276 278
0 2 8 12 26 30 32 36 38 42 50 56 60 68 72 78 80 86 92 96 98 102 108 116 138 140 162 170 176 180 182 186 192 198 200 206 210 218 222 228 236 240 242 246 248 252 266 270 276 278
0 2 8 12 26 30 32 38 42 50 56 60 66 68 72 78 80 86 92 96 98 102 108 120 138 140 158 170 176 180 182 186 192 198 200 206 210 212 218 222 228 236 240 246 248 252 266 270 276 278
0 2 8 12 26 32 36 38 42 50 56 60 66 68 72 78 80 86 92 96 98 102 108 116 138 140 162 170 176 180 182 186 192 198 200 206 210 212 218 222 228 236 240 242 246 252 266 270 276 278
0 2 8 12 26 32 38 42 50 56 60 66 68 72 78 80 86 92 96 98 102 108 116 120 138 140 158 162 170 176 180 182 186 192 198 200 206 210 212 218 222 228 236 240 246 252 266 270 276 278
0 2 8 26 30 32 38 42 50 56 60 66 68 72 78 80 86 92 96 98 102 108 116 120 138 140 158 162 170 176 180 182 186 192 198 200 206 210 212 218 222 228 236 240 246 248 252 270 276 278
0 2 12 26 30 32 36 38 42 50 56 60 66 68 72 78 80 92 96 98 102 108 110 116 138 140 162 168 170 176 180 182 186 198 200 206 210 212 218 222 228 236 240 242 246 248 252 266 276 278
0 2 12 26 30 32 36 38 42 50 60 66 68 72 78 80 92 96 98 102 108 110 116 122 138 140 156 162 168 170 176 180 182 186 198 200 206 210 212 218 228 236 240 242 246 248 252 266 276 278
0 2 12 26 30 32 38 42 50 56 60 66 68 72 78 80 92 96 98 102 108 110 116 120 138 140 158 162 168 170 176 180 182 186 198 200 206 210 212 218 222 228 236 240 246 248 252 266 276 278

отсюда
https://oeis.org/A266512/a266512_1.txt

Это мы с коллегой Владимиром Чирковым постарались :)
Я начала, а он продолжил.

gris
для вас задачка, вы ведь скучаете по кортежам :)

А мне другая задача уже несколько дней покоя не даёт, свербит и свербит.
Я уж и так, и сяк прикидывала, пока не уловлю чёткую схему.
Но чувствую, что должен быть алгоритм.

Программа поиска центральных 16-ок в 18-ах - 30-ах с минимальным диаметром (11 различных паттернов)

\l res_16tuple_new1.txt
{m=[5843, 10463, 19493, 24113];
s=[6889, 23059];
t=[1219, 5839, 10459, 14869, 15079, 19489, 24109, 28729];
u=[5839, 8149, 10459, 19489, 21799, 24109];
o=[11509, 18439];
y=[3319, 5839, 10249, 10459, 19489, 19699, 24109, 26629];
q=[9197, 20747];
r=[8147, 21797, 29987];

pat=[0, 6, 8, 14, 18, 24, 26, 36, 38, 48, 50, 56, 60, 66, 68, 74];
pat1=vector(16); w=vector(24);
pat2=[36, 38];
pat4=[26, 36, 38, 48];
pat6=[24, 26, 36, 38, 48, 50];
pat8=[18, 24, 26, 36, 38, 48, 50, 56];
pat10=[14, 18, 24, 26, 36, 38, 48, 50, 56, 60];
pat12=[8, 14, 18, 24, 26, 36, 38, 48, 50, 56, 60, 66];
pat14=[6, 8, 14, 18, 24, 26, 36, 38, 48, 50, 56, 60, 66, 68];
w2=vector(2); w4=vector(4); w6=vector(6); w8=vector(8); w10=vector(10); w12=vector(12); w14=vector(14);

pata=[0, 4, 10, 12, 18, 22, 24, 28, 54, 58, 60, 64, 70, 72, 78, 82];
pata1=vector(16); wa=vector(24);
pata2=[28, 54];
pata4=[24, 28, 54, 58];
pata6=[22, 24, 28, 54, 58, 60];
pata8=[18, 22, 24, 28, 54, 58, 60, 64];
pata10=[12, 18, 22, 24, 28, 54, 58, 60, 64, 70];
pata12=[10, 12, 18, 22, 24, 28, 54, 58, 60, 64, 70, 72];
pata14=[4, 10, 12, 18, 22, 24, 28, 54, 58, 60, 64, 70, 72, 78];
wa14=vector(14); wa12=vector(12); wa10=vector(10); wa8=vector(8); wa6=vector(6); wa4=vector(4); wa2=vector(2);

patb=[0, 4, 10, 12, 18, 22, 28, 30, 52, 54, 60, 64, 70, 72, 78, 82];
patb1=vector(16); wb=vector(24);
patb2=[30, 52];
patb4=[28, 30, 52, 54];
patb6=[22, 28, 30, 52, 54, 60];
patb8=[18, 22, 28, 30, 52, 54, 60, 64];
patb10=[12, 18, 22, 28, 30, 52, 54, 60, 64, 70];
patb12=[10, 12, 18, 22, 28, 30, 52, 54, 60, 64, 70, 72];
patb14=[4, 10, 12, 18, 22, 28, 30, 52, 54, 60, 64, 70, 72, 78];
wb14=vector(14); wb12=vector(12); wb10=vector(10); wb8=vector(8); wb6=vector(6); wb4=vector(4); wb2=vector(2);

patc=[0, 4, 10, 12, 18, 22, 30, 40, 42, 52, 60, 64, 70, 72, 78, 82];
patc1=vector(16); wc=vector(24);
patc2=[40, 42];
patc4=[30, 40, 42, 52];
patc6=[22, 30, 40, 42, 52, 60];
patc8=[18, 22, 30, 40, 42, 52, 60, 64];
patc10=[12, 18, 22, 30, 40, 42, 52, 60, 64, 70];
patc12=[10, 12, 18, 22, 30, 40, 42, 52, 60, 64, 70, 72];
patc14=[4, 10, 12, 18, 22, 30, 40, 42, 52, 60, 64, 70, 72, 78];
wc14=vector(14); wc12=vector(12); wc10=vector(10); wc8=vector(8); wc6=vector(6); wc4=vector(4); wc2=vector(2);

patd=[0, 4, 10, 12, 18, 24, 28, 40, 42, 54, 58, 64, 70, 72, 78, 82];
patd1=vector(16); wd=vector(24);
patd2=[40, 42];
patd4=[28, 40, 42, 54];
patd6=[24, 28, 40, 42, 54, 58];
patd8=[18, 24, 28, 40, 42, 54, 58, 64];
patd10=[12, 18, 24, 28, 40, 42, 54, 58, 64, 70];
patd12=[10, 12, 18, 24, 28, 40, 42, 54, 58, 64, 70, 72];
patd14=[4, 10, 12, 18, 24, 28, 40, 42, 54, 58, 64, 70, 72, 78];
wd14=vector(14); wd12=vector(12); wd10=vector(10); wd8=vector(8); wd6=vector(6); wd4=vector(4); wd2=vector(2);

pate=[0, 4, 10, 12, 18, 28, 30, 40, 42, 52, 54, 64, 70, 72, 78, 82];
pate1=vector(16); we=vector(24);
pate2=[40, 42];
pate4=[30, 40, 42, 52];
pate6=[28, 30, 40, 42, 52, 54];
pate8=[18, 28, 30, 40, 42, 52, 54, 64];
pate10=[12, 18, 28, 30, 40, 42, 52, 54, 64, 70];
pate12=[10, 12, 18, 28, 30, 40, 42, 52, 54, 64, 70, 72];
pate14=[4, 10, 12, 18, 28, 30, 40, 42, 52, 54, 64, 70, 72, 78];
we14=vector(14); we12=vector(12); we10=vector(10); we8=vector(8); we6=vector(6); we4=vector(4); we2=vector(2);

patf=[0, 2, 6, 12, 24, 26, 30, 42, 44, 56, 60, 62, 74, 80, 84, 86];
patf1=vector(16); wf=vector(24);
patf2=[42, 44];
patf4=[30, 42, 44, 56];
patf6=[26, 30, 42, 44, 56, 60];
patf8=[24, 26, 30, 42, 44, 56, 60, 62];
patf10=[12, 24, 26, 30, 42, 44, 56, 60, 62, 74];
patf12=[6, 12, 24, 26, 30, 42, 44, 56, 60, 62, 74, 80];
patf14=[2, 6, 12, 24, 26, 30, 42, 44, 56, 60, 62, 74, 80, 84];
wf14=vector(14); wf12=vector(12); wf10=vector(10); wf8=vector(8); wf6=vector(6); wf4=vector(4); wf2=vector(2);

patg=[0, 2, 6, 12, 14, 20, 24, 42, 44, 62, 66, 72, 74, 80, 84, 86];
patg1=vector(16); wg=vector(24);
patg2=[42, 44];
patg4=[24, 42, 44, 62];
patg6=[20, 24, 42, 44, 62, 66];
patg8=[14, 20, 24, 42, 44, 62, 66, 72];
patg10=[12, 14, 20, 24, 42, 44, 62, 66, 72, 74];
patg12=[6, 12, 14, 20, 24, 42, 44, 62, 66, 72, 74, 80];
patg14=[2, 6, 12, 14, 20, 24, 42, 44, 62, 66, 72, 74, 80, 84];
wg14=vector(14); wg12=vector(12); wg10=vector(10); wg8=vector(8); wg6=vector(6); wg4=vector(4); wg2=vector(2);

path=[0, 2, 6, 12, 14, 24, 26, 42, 44, 60, 62, 72, 74, 80, 84, 86];
path1=vector(16); wh=vector(24);
path2=[42, 44];
path4=[26, 42, 44, 60];
path6=[24, 26, 42, 44, 60, 62];
path8=[14, 24, 26, 42, 44, 60, 62, 72];
path10=[12, 14, 24, 26, 42, 44, 60, 62, 72, 74];
path12=[6, 12, 14, 24, 26, 42, 44, 60, 62, 72, 74, 80];
path14=[2, 6, 12, 14, 24, 26, 42, 44, 60, 62, 72, 74, 80, 84];
wh14=vector(14); wh12=vector(12); wh10=vector(10); wh8=vector(8); wh6=vector(6); wh4=vector(4); wh2=vector(2);

patl=[0, 2, 6, 12, 20, 24, 26, 42, 44, 60, 62, 66, 74, 80, 84, 86];
patl1=vector(16); wl=vector(24);
patl2=[42, 44];
patl4=[26, 42, 44, 60];
patl6=[24, 26, 42, 44, 60, 62];
patl8=[20, 24, 26, 42, 44, 60, 62, 66];
patl10=[12, 20, 24, 26, 42, 44, 60, 62, 66, 74];
patl12=[6, 12, 20, 24, 26, 42, 44, 60, 62, 66, 74, 80];
patl14=[2, 6, 12, 20, 24, 26, 42, 44, 60, 62, 66, 74, 80, 84];
wl14=vector(14); wl12=vector(12); wl10=vector(10); wl8=vector(8); wl6=vector(6); wl4=vector(4); wl2=vector(2);

patp=[0, 4, 10, 12, 18, 22, 24, 40, 42, 58, 60, 64, 70, 72, 78, 82];
patp1=vector(16); wp=vector(24);
patp2=[40, 42];
patp4=[24, 40, 42, 58];
patp6=[22, 24, 40, 42, 58, 60];
patp8=[18, 22, 24, 40, 42, 58, 60, 64];
patp10=[12, 18, 22, 24, 40, 42, 58, 60, 64, 70];
patp12=[10, 12, 18, 22, 24, 40, 42, 58, 60, 64, 70, 72];
patp14=[4, 10, 12, 18, 22, 24, 40, 42, 58, 60, 64, 70, 72, 78];
wp14=vector(14); wp12=vector(12); wp10=vector(10); wp8=vector(8); wp6=vector(6); wp4=vector(4); wp2=vector(2);


i1=614278040000001+29*10^8+40*10^7+10^9+14*10^10;
i2=i1-1+2*10^10;

print("range of search");
print(i1," (p=", i1*30030," )");
print(i2," (p=", i2*30030," )");

forstep (i=i1,i2,999,
x=30030*i;
for (n=1,4,
v=x+m[n];
if(ispseudoprime(v) && ispseudoprime(v+74),
k=0; 
forprime(p=v,v+74, k++; w[k]=p; );
if(k==16,
for(j=1,16, pat1[j]=w[j]-w[1]; ); print(pat1);
for(m=1,2, w2[m]=pat1[m+7]; );
for(m=1,4, w4[m]=pat1[m+6]; );
for(m=1,6, w6[m]=pat1[m+5]; );
for(m=1,8, w8[m]=pat1[m+4]; );
for(m=1,10, w10[m]=pat1[m+3]; );
for(m=1,12, w12[m]=pat1[m+2]; );
for(m=1,14, w14[m]=pat1[m+1]; );
if(w2==pat2, print(w[8],": ",w2); print(w[1],": ",pat1); );
if(w4==pat4, print(w[7],": ",w4); print(w[1],": ",pat1); );
if(w6==pat6, print(w[6],": ",w6); print(w[1],": ",pat1); );
if(w8==pat8, print(w[5],": ",w8); print(w[1],": ",pat1); );
if(w10==pat10, print(w[4],": ",w10); print(w[1],": ",pat1); );
if(w12==pat12, print(w[3],": ",w12); print(w[1],": ",pat1); );
if(w14==pat14, print(w[2],": ",w14); print(w[1],": ",pat1); );
);););

for (n=1,8,
v=x+t[n];
if(ispseudoprime(v) && ispseudoprime(v+82),
k=0; 
forprime(p=v,v+82, k++; wb[k]=p; );
if(k==16,
for(j=1,16, patb1[j]=wb[j]-wb[1]; ); print(patb1);
for(m=1,2, wb2[m]=patb1[m+7]; );
for(m=1,4, wb4[m]=patb1[m+6]; );
for(m=1,6, wb6[m]=patb1[m+5]; );
for(m=1,8, wb8[m]=patb1[m+4]; );
for(m=1,10, wb10[m]=patb1[m+3]; );
for(m=1,12, wb12[m]=patb1[m+2]; );
for(m=1,14, wb14[m]=patb1[m+1]; );
if(wb2==patb2, print(wb[8],": ",wb2); print(wb[1],": ",patb1); );
if(wb4==patb4, print(wb[7],": ",wb4); print(wb[1],": ",patb1); );
if(wb6==patb6, print(wb[6],": ",wb6); print(wb[1],": ",patb1); );
if(wb8==patb8, print(wb[5],": ",wb8); print(wb[1],": ",patb1); );
if(wb10==patb10, print(wb[4],": ",wb10); print(wb[1],": ",patb1); );
if(wb12==patb12, print(wb[3],": ",wb12); print(wb[1],": ",patb1); );
if(wb14==patb14, print(wb[2],": ",wb14); print(wb[1],": ",patb1); );
););

v=x+y[n];
if(ispseudoprime(v) && ispseudoprime(v+82),
k=0; 
forprime(p=v,v+82, k++; we[k]=p; );
if(k==16,
for(j=1,16, pate1[j]=we[j]-we[1]; ); print(pate1);
for(m=1,2, we2[m]=pate1[m+7]; );
for(m=1,4, we4[m]=pate1[m+6]; );
for(m=1,6, we6[m]=pate1[m+5]; );
for(m=1,8, we8[m]=pate1[m+4]; );
for(m=1,10, we10[m]=pate1[m+3]; );
for(m=1,12, we12[m]=pate1[m+2]; );
for(m=1,14, we14[m]=pate1[m+1]; );
if(we2==pate2, print(we[8],": ",we2); print(we[1],": ",pate1); );
if(we4==pate4, print(we[7],": ",we4); print(we[1],": ",pate1); );
if(we6==pate6, print(we[6],": ",we6); print(we[1],": ",pate1); );
if(we8==pate8, print(we[5],": ",we8); print(we[1],": ",pate1); );
if(we10==pate10, print(we[4],": ",we10); print(we[1],": ",pate1); );
if(we12==pate12, print(we[3],": ",we12); print(we[1],": ",pate1); );
if(we14==pate14, print(we[2],": ",we14); print(we[1],": ",pate1); );
);););

for (n=1,6,
v=x+u[n];
if(ispseudoprime(v) && ispseudoprime(v+82),
k=0; 
forprime(p=v,v+82, k++; wc[k]=p; );
if(k==16,
for(j=1,16, patc1[j]=wc[j]-wc[1]; ); print(patc1);
for(m=1,2, wc2[m]=patc1[m+7]; );
for(m=1,4, wc4[m]=patc1[m+6]; );
for(m=1,6, wc6[m]=patc1[m+5]; );
for(m=1,8, wc8[m]=patc1[m+4]; );
for(m=1,10, wc10[m]=patc1[m+3]; );
for(m=1,12, wc12[m]=patc1[m+2]; );
for(m=1,14, wc14[m]=patc1[m+1]; );
if(wc2==patc2, print(wc[8],": ",wc2); print(wc[1],": ",patc1); );
if(wc4==patc4, print(wc[7],": ",wc4); print(wc[1],": ",patc1); );
if(wc6==patc6, print(wc[6],": ",wc6); print(wc[1],": ",patc1); );
if(wc8==patc8, print(wc[5],": ",wc8); print(wc[1],": ",patc1); );
if(wc10==patc10, print(wc[4],": ",wc10); print(wc[1],": ",patc1); );
if(wc12==patc12, print(wc[3],": ",wc12); print(wc[1],": ",patc1); );
if(wc14==patc14, print(wc[2],": ",wc14); print(wc[1],": ",patc1); );
);););

for (n=1,2,
v=x+s[n];
if(ispseudoprime(v) && ispseudoprime(v+82),
k=0; 
forprime(p=v,v+82, k++; wa[k]=p; );
if(k==16,
for(j=1,16, pata1[j]=wa[j]-wa[1]; ); print(pata1);
for(m=1,2, wa2[m]=pata1[m+7]; );
for(m=1,4, wa4[m]=pata1[m+6]; );
for(m=1,6, wa6[m]=pata1[m+5]; );
for(m=1,8, wa8[m]=pata1[m+4]; );
for(m=1,10, wa10[m]=pata1[m+3]; );
for(m=1,12, wa12[m]=pata1[m+2]; );
for(m=1,14, wa14[m]=pata1[m+1]; );
if(wa2==pata2, print(wa[8],": ",wa2); print(wa[1],": ",pata1); );
if(wa4==pata4, print(wa[7],": ",wa4); print(wa[1],": ",pata1); );
if(wa6==pata6, print(wa[6],": ",wa6); print(wa[1],": ",pata1); );
if(wa8==pata8, print(wa[5],": ",wa8); print(wa[1],": ",pata1); );
if(wa10==pata10, print(wa[4],": ",wa10); print(wa[1],": ",pata1); );
if(wa12==pata12, print(wa[3],": ",wa12); print(wa[1],": ",pata1); );
if(wa14==pata14, print(wa[2],": ",wa14); print(wa[1],": ",pata1); );
););

v=x+o[n];
if(ispseudoprime(v) && ispseudoprime(v+82),
k=0;
forprime(p=v,v+82, k++; wd[k]=p; );
if(k==16,
for(j=1,16, patd1[j]=wd[j]-wd[1]; ); print(patd1);
for(m=1,2, wd2[m]=patd1[m+7]; );
for(m=1,4, wd4[m]=patd1[m+6]; );
for(m=1,6, wd6[m]=patd1[m+5]; );
for(m=1,8, wd8[m]=patd1[m+4]; );
for(m=1,10, wd10[m]=patd1[m+3]; );
for(m=1,12, wd12[m]=patd1[m+2]; );
for(m=1,14, wd14[m]=patd1[m+1]; );
if(wd2==patd2, print(wd[8],": ",wd2); print(wd[1],": ",patd1); );
if(wd4==patd4, print(wd[7],": ",wd4); print(wd[1],": ",patd1); );
if(wd6==patd6, print(wd[6],": ",wd6); print(wd[1],": ",patd1); );
if(wd8==patd8, print(wd[5],": ",wd8); print(wd[1],": ",patd1); );
if(wd10==patd10, print(wd[4],": ",wd10); print(wd[1],": ",patd1); );
if(wd12==patd12, print(wd[3],": ",wd12); print(wd[1],": ",patd1); );
if(wd14==patd14, print(wd[2],": ",wd14); print(wd[1],": ",patd1); );
););

v=x+q[n];
if(ispseudoprime(v) && ispseudoprime(v+86),
k=0;
forprime(p=v,v+86, k++; wf[k]=p; );
if(k==16,
for(j=1,16, patf1[j]=wf[j]-wf[1]; ); print(patf1);
for(m=1,2, wf2[m]=patf1[m+7]; );
for(m=1,4, wf4[m]=patf1[m+6]; );
for(m=1,6, wf6[m]=patf1[m+5]; );
for(m=1,8, wf8[m]=patf1[m+4]; );
for(m=1,10, wf10[m]=patf1[m+3]; );
for(m=1,12, wf12[m]=patf1[m+2]; );
for(m=1,14, wf14[m]=patf1[m+1]; );
if(wf2==patf2, print(wf[8],": ",wf2); print(wf[1],": ",patf1); );
if(wf4==patf4, print(wf[7],": ",wf4); print(wf[1],": ",patf1); );
if(wf6==patf6, print(wf[6],": ",wf6); print(wf[1],": ",patf1); );
if(wf8==patf8, print(wf[5],": ",wf8); print(wf[1],": ",patf1); );
if(wf10==patf10, print(wf[4],": ",wf10); print(wf[1],": ",patf1); );
if(wf12==patf12, print(wf[3],": ",wf12); print(wf[1],": ",patf1); );
if(wf14==patf14, print(wf[2],": ",wf14); print(wf[1],": ",patf1); );
);););

for (n=1,3,
v=x+r[n];
if(ispseudoprime(v) && ispseudoprime(v+86),
k=0;
forprime(p=v,v+86, k++; wg[k]=p; );
if(k==16,
for(j=1,16, patg1[j]=wg[j]-wg[1]; ); print(patg1);
for(m=1,2, wg2[m]=patg1[m+7]; );
for(m=1,4, wg4[m]=patg1[m+6]; );
for(m=1,6, wg6[m]=patg1[m+5]; );
for(m=1,8, wg8[m]=patg1[m+4]; );
for(m=1,10, wg10[m]=patg1[m+3]; );
for(m=1,12, wg12[m]=patg1[m+2]; );
for(m=1,14, wg14[m]=patg1[m+1]; );
if(wg2==patg2, print(wg[8],": ",wg2); print(wg[1],": ",patg1); );
if(wg4==patg4, print(wg[7],": ",wg4); print(wg[1],": ",patg1); );
if(wg6==patg6, print(wg[6],": ",wg6); print(wg[1],": ",patg1); );
if(wg8==patg8, print(wg[5],": ",wg8); print(wg[1],": ",patg1); );
if(wg10==patg10, print(wg[4],": ",wg10); print(wg[1],": ",patg1); );
if(wg12==patg12, print(wg[3],": ",wg12); print(wg[1],": ",patg1); );
if(wg14==patg14, print(wg[2],": ",wg14); print(wg[1],": ",patg1); );
);););

v=x+29987;
if(ispseudoprime(v) && ispseudoprime(v+86),
k=0;
forprime(p=v,v+86, k++; wh[k]=p; );
if(k==16,
for(j=1,16, path1[j]=wh[j]-wh[1]; ); print(path1);
for(m=1,2, wh2[m]=path1[m+7]; );
for(m=1,4, wh4[m]=path1[m+6]; );
for(m=1,6, wh6[m]=path1[m+5]; );
for(m=1,8, wh8[m]=path1[m+4]; );
for(m=1,10, wh10[m]=path1[m+3]; );
for(m=1,12, wh12[m]=path1[m+2]; );
for(m=1,14, wh14[m]=path1[m+1]; );
if(wh2==path2, print(wh[8],": ",wh2); print(wh[1],": ",path1); );
if(wh4==path4, print(wh[7],": ",wh4); print(wh[1],": ",path1); );
if(wh6==path6, print(wh[6],": ",wh6); print(wh[1],": ",path1); );
if(wh8==path8, print(wh[5],": ",wh8); print(wh[1],": ",path1); );
if(wh10==path10, print(wh[4],": ",wh10); print(wh[1],": ",path1); );
if(wh12==path12, print(wh[3],": ",wh12); print(wh[1],": ",path1); );
if(wh14==path14, print(wh[2],": ",wh14); print(wh[1],": ",path1); );
););

v=x+29987;
if(ispseudoprime(v) && ispseudoprime(v+86),
k=0;
forprime(p=v,v+86, k++; wl[k]=p; );
if(k==16,
for(j=1,16, patl1[j]=wl[j]-wl[1]; ); print(patl1);
for(m=1,2, wl2[m]=patl1[m+7]; );
for(m=1,4, wl4[m]=patl1[m+6]; );
for(m=1,6, wl6[m]=patl1[m+5]; );
for(m=1,8, wl8[m]=patl1[m+4]; );
for(m=1,10, wl10[m]=patl1[m+3]; );
for(m=1,12, wl12[m]=patl1[m+2]; );
for(m=1,14, wl14[m]=patl1[m+1]; );
if(wl2==patl2, print(wl[8],": ",wl2); print(wl[1],": ",patl1); );
if(wl4==patl4, print(wl[7],": ",wl4); print(wl[1],": ",patl1); );
if(wl6==patl6, print(wl[6],": ",wl6); print(wl[1],": ",patl1); );
if(wl8==patl8, print(wl[5],": ",wl8); print(wl[1],": ",patl1); );
if(wl10==patl10, print(wl[4],": ",wl10); print(wl[1],": ",patl1); );
if(wl12==patl12, print(wl[3],": ",wl12); print(wl[1],": ",patl1); );
if(wl14==patl14, print(wl[2],": ",wl14); print(wl[1],": ",patl1); );
););

v=x+29989;
if(ispseudoprime(v) && ispseudoprime(v+82),
k=0;
forprime(p=v,v+82, k++; wp[k]=p; );
if(k==16,
for(j=1,16, patp1[j]=wp[j]-wp[1]; ); print(patp1);
for(m=1,2, wp2[m]=patp1[m+7]; );
for(m=1,4, wp4[m]=patp1[m+6]; );
for(m=1,6, wp6[m]=patp1[m+5]; );
for(m=1,8, wp8[m]=patp1[m+4]; );
for(m=1,10, wp10[m]=patp1[m+3]; );
for(m=1,12, wp12[m]=patp1[m+2]; );
for(m=1,14, wp14[m]=patp1[m+1]; );
if(wp2==patp2, print(wp[8],": ",wp2); print(wp[1],": ",patp1); );
if(wp4==patp4, print(wp[7],": ",wp4); print(wp[1],": ",patp1); );
if(wp6==patp6, print(wp[6],": ",wp6); print(wp[1],": ",patp1); );
if(wp8==patp8, print(wp[5],": ",wp8); print(wp[1],": ",patp1); );
if(wp10==patp10, print(wp[4],": ",wp10); print(wp[1],": ",patp1); );
if(wp12==patp12, print(wp[3],": ",wp12); print(wp[1],": ",patp1); );
if(wp14==patp14, print(wp[2],": ",wp14); print(wp[1],": ",patp1); );
););
);
}

Вот эта версия прямо сейчас работает на черепашке.
Жадность алгоритма задаётся в строке

forstep (i=i1,i2,999,

Чтобы вернуться к обычному (не жадному) алгоритму, запишите эту строку так

for (i=i1,i2,

Тогда поиск будет тотальный, пропусков не будет.
То есть это брутфорс - поиск 16-ок по паттерну.

Программа длинная, на экране проверять трудно.
Распечатать не удаётся. У меня принтер что-то с ума сошёл; задаю ему, например, распечатать текстовый файл, а он мне печатает сообщения с форума BOINC-проекта ОДЛК.
И что только я ни делала, всё очищала в памяти принтера, все флаги снимала.
Ничего не помогает!
Привязался намертво к форуму :(
Может, кто-нибудь знает, как его отвязать от форума?

Поэтому просьба, господа!
Если ошибку обнаружите в программе, сообщите, пожалуйста.

Программу тестировала на известных центральных 16-ах, тест успешно выполняется.
Но!
Ни одного другого решения программа пока не нашла.

Если у вас ОС Windows 64-bit, вы можете попробовать программу.
Запуск в программной оболочке PARI/GP.

Может, будет и в 32-bit работать, не знаю, у меня 64-bit.

Интервал поиска задаётся в строках

i1=614278040000001+29*10^8+40*10^7+10^9+14*10^10;
i2=i1-1+2*10^10;

Сейчас сделала для черепашки длину интервала 2*10^10.
Такой интервал она обсчитывает (при указанной жадности алгоритма) примерно за 2,5 часа.
Реальный интервал будет совсем другой.
Вот

(12:18) gp > \r 16tuple_new1.txt
   logfile = "res_16tuple_new1.txt"
range of search
614422340000001 (p=18451102870200030030 )
614442340000000 (p=18451703470200000000 )

Реальный интервал смотрите в скобках.

Также приветствуется любая оптимизация программы.
Пожалуйста, пишите мне.
Адрес прежний.

Особая просьба к wrest, хотя... gris говорил мне, что он (wrest) не любит кортежи.
Ну, кортежи пусть не любит (я буду любить их за двоих), а программу же можно оптимизировать :)

Вот и закончился проход на черепашке по показанной программе

(12:18) gp > \r 16tuple_new1.txt
   logfile = "res_16tuple_new1.txt"
range of search
614422340000001 (p=18451102870200030030 )
614442340000000 (p=18451703470200000000 )
time = 2h, 33min, 39,972 ms.

Тут вы видите время выполнения программы.

А решений по-прежнему нет :(