First results!

Message boards : Science : First results!

To post messages, you must log in.

AuthorMessage
256Ghz
Project administrator
Avatar

Send message
Joined: 8 Feb 17
Posts: 68
Credit: 23,218,083
RAC: 33,924
Message 81 - Posted: 15 Mar 2017, 13:50:21 UTC
Last modified: 15 Mar 2017, 13:56:47 UTC

ID: 81 · Rating: 0 · rate: Rate + / Rate - Report as offensive    Reply Quote
Profile Natalia Makarova
Avatar

Send message
Joined: 5 Mar 17
Posts: 70
Credit: 0
RAC: 0
Message 82 - Posted: 15 Mar 2017, 19:50:12 UTC - in response to Message 81.  
Last modified: 15 Mar 2017, 19:53:13 UTC

Good work!
However, no significant new solutions have been found so far: for k = 17, 19, 21, 23, 25, 26.
ID: 82 · Rating: 0 · rate: Rate + / Rate - Report as offensive    Reply Quote
Profile Natalia Makarova
Avatar

Send message
Joined: 5 Mar 17
Posts: 70
Credit: 0
RAC: 0
Message 83 - Posted: 15 Mar 2017, 21:20:11 UTC - in response to Message 81.  

I see in the database all the solutions for k = 24, found in my project

22930603692243271: 0 70 76 118 136 156 160 178 202 222 238 250 378 390 406 426 450 468 472 492 510 552 558 628 (V. Danilov)
34984922852185283: 0 26 66 74 80 96 104 126 204 206 216 236 258 278 288 290 368 390 398 414 420 428 468 494 (A. Andreyev)
60960572612579749: 0 30 58 64 72 82 84 102 120 154 160 174 238 252 258 292 310 328 330 340 348 354 382 412 (dimych)
ID: 83 · Rating: 0 · rate: Rate + / Rate - Report as offensive    Reply Quote
Profile Natalia Makarova
Avatar

Send message
Joined: 5 Mar 17
Posts: 70
Credit: 0
RAC: 0
Message 84 - Posted: 15 Mar 2017, 21:42:20 UTC

We see in the OEIS sequence

Magic constants of 4 X 4 pandiagonal magic squares composed of consecutive primes.
http://oeis.org/A256234

682775764735680, 47184892811061120, 50194833750826260, 70151123608154420, 76685404549625256, 93295105984206480, 94615738903617540, 123483356772380760, 141536742113504220, 211283804186719200, 214070508927033000

The last solution
#11 (author D. Ivanov)

53517627231758089 +
0 292 138 214
208 144 70 222
184 108 322 30
252 100 114 178

S=214070508927033000

A list of the nearest solutions by J. Wroblewski that need to be confirmed

64 357 903 328 718 397: 0,6,10,16,126,132,136,142,144,150,154,160,270,276,280,286
64 747 964 125 739 269: 0,12,30,42,58,60,70,72,88,90,100,102,118,130,148,160
65 659 672 001 596 307: 0,24,60,66,84,90,116,126,140,150,176,182,200,206,242,266
75 219 020 808 006 217: 0,6,36,42,70,76,106,112,114,120,150,156,184,190,220,226
78 083 002 410 887 917: 0,46,60,66,106,112,126,150,172,196,210,216,256,262,276,322
87 883 992 459 664 963: 0,46,60,84,90,106,130,136,144,150,174,190,196,220,234,280
90 658 333 138 283 839: 0,40,42,48,82,88,90,130,132,172,174,180,214,220,222,262

Are there any omitted solutions?

See
http://oeis.org/A256234/a256234_2.txt
ID: 84 · Rating: 0 · rate: Rate + / Rate - Report as offensive    Reply Quote
256Ghz
Project administrator
Avatar

Send message
Joined: 8 Feb 17
Posts: 68
Credit: 23,218,083
RAC: 33,924
Message 85 - Posted: 16 Mar 2017, 8:16:29 UTC
Last modified: 8 Apr 2017, 16:36:36 UTC

Founded sequences:

n=16, 170693941183817:   0 30 42 44 72 74 86 90 116 120 132 134 162 164 176 206
n=16, 11796223202765101: 0 22 36 58 90 112 126 148 210 232 246 268 300 322 336 358
n=16, 12548708437706431: 0 12 18 28 30 40 46 58 210 222 228 238 240 250 256 268
n=16, 17537780902038437: 0 6 60 66 126 132 144 150 186 192 204 210 270 276 330 336 "sexy"
n=16, 19171351137406219: 0 22 30 48 52 70 78 90 100 112 120 138 142 160 168 190
n=16, 23323776496051501: 0 30 42 66 72 96 100 108 130 138 142 166 172 196 208 238
n=16, 23653934725904299: 0 12 22 34 48 60 70 82 90 102 112 124 138 150 160 172 "double sexy"
n=16, 30870839193095093: 0 14 30 44 66 80 84 96 98 110 114 128 150 164 180 194  "double seven" 
n=16, 35384185528375907: 0 26 60 84 86 110 126 144 152 170 186 210 212 236 270 296
n=16, 52820951046679703: 0 20 24 44 66 84 86 90 104 108 110 128 150 170 174 194
n=16, 53517627231758089: 0 30 70 100 108 114 138 144 178 184 208 214 222 252 292 322
n=16, 64357903328718397: 0 6 10 16 126 132 136 142 144 150 154 160 270 276 280 286   "sexy"
n=16, 64747964125739269: 0 12 30 42 58 60 70 72 88 90 100 102 118 130 148 160 "double sexy"
n=16, 65659672001596307: 0 24 60 66 84 90 116 126 140 150 176 182 200 206 242 266
n=16, 75219020808006217: 0 6 36 42 70 76 106 112 114 120 150 156 184 190 220 226 "sexy"
n=16, 78083002410887917: 0 46 60 66 106 112 126 150 172 196 210 216 256 262 276 322 
n=16, 87883992459664963: 0 46 60 84 90 106 130 136 144 150 174 190 196 220 234 280
n=16, 90658333138283839: 0 40 42 48 82 88 90 130 132 172 174 180 214 220 222 262



Nothing new, all interesting soon :)
ID: 85 · Rating: 0 · rate: Rate + / Rate - Report as offensive    Reply Quote
Profile Natalia Makarova
Avatar

Send message
Joined: 5 Mar 17
Posts: 70
Credit: 0
RAC: 0
Message 86 - Posted: 16 Mar 2017, 9:22:15 UTC - in response to Message 85.  

Thank you.
Really very interesting!
Hence, all decisions of J. Wroblewski are confirmed in this range.
There are no omissions.
Excellent!

You can add these solutions in sequence A256234
You can write that the solutions are found in the BOINC-project.
ID: 86 · Rating: 0 · rate: Rate + / Rate - Report as offensive    Reply Quote

Message boards : Science : First results!

©2017 by 256Ghz