Cody

Problem 44403. Goldbach's marginal conjecture - Write integer as sum of three primes

Solution 2243375

Submitted on 29 Apr 2020 by Simone Corti
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Test Suite

Test Status Code Input and Output
1   Pass
n = 6; y = goldbach3(n); y_correct = [2,2,2]; assert(isequal(y,y_correct))

x = 2 3 5 y = 2 2 2

2   Pass
n = 7; y = goldbach3(n); y_correct = [2,2,3]; assert(isequal(y,y_correct))

x = 2 3 5 7 y = 2 2 3

3   Pass
n = 8; y = goldbach3(n); y_correct = [2,3,3]; assert(isequal(y,y_correct))

x = 2 3 5 7 y = 2 3 3

4   Pass
n = 9; y = goldbach3(n); y_correct1 = [2,2,5]; y_correct2 = [3,3,3]; assert(isequal(y,y_correct1)|isequal(y,y_correct2))

x = 2 3 5 7 y = 2 2 5

5   Pass
n = 10; y = goldbach3(n); y_correct = [2,3,5]; assert(isequal(y,y_correct))

x = 2 3 5 7 y = 2 3 5

6   Pass
n = 11; y = goldbach3(n); y_correct1 = [2,2,7]; y_correct2 = [3,3,5]; assert(isequal(y,y_correct1)|isequal(y,y_correct2))

x = 2 3 5 7 11 y = 2 2 7

7   Pass
n = 12; y = goldbach3(n); y_correct1 = [2,3,7]; y_correct2 = [2,5,5]; assert(isequal(y,y_correct1)|isequal(y,y_correct2))

x = 2 3 5 7 11 y = 2 3 7

8   Pass
n = 13; y = goldbach3(n); y_correct1 = [3,3,7]; y_correct2 = [3,5,5]; assert(isequal(y,y_correct1)|isequal(y,y_correct2))

x = 2 3 5 7 11 13 y = 3 3 7

9   Pass
n = 14; y = goldbach3(n); y_correct = [2,5,7]; assert(isequal(y,y_correct))

x = 2 3 5 7 11 13 y = 2 5 7

10   Pass
n = 15; y = goldbach3(n); y_correct1 = [2,2,11]; y_correct2 = [3,5,7]; y_correct3 = [5,5,5]; assert(isequal(y,y_correct1)|isequal(y,y_correct2)|isequal(y,y_correct3))

x = 2 3 5 7 11 13 y = 2 2 11

11   Pass
n = 101; y = goldbach3(n); assert(isequal(y,sort(y))) assert(all(isprime(y))) assert(sum(y)==n)

x = 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 y = 2 2 97

12   Pass
n = 102; y = goldbach3(n); assert(isequal(y,sort(y))) assert(all(isprime(y))) assert(sum(y)==n)

x = 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 y = 2 3 97

13   Pass
for n = 250:300 y = goldbach3(n); assert(isequal(y,sort(y))); assert(all(isprime(y))); assert(sum(y)==n); end

x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 53 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 y = 2 7 241 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 54 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 y = 3 7 241 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 54 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 y = 2 11 239 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 54 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 y = 3 11 239 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 54 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 y = 2 11 241 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 54 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 y = 2 2 251 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 54 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 y = 2 3 251 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 55 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 y = 3 3 251 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 55 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 y = 2 5 251 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 55 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 y = 3 5 251 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 55 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 y = 2 7 251 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 55 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 y = 2 2 257 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 55 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 y = 2 3 257 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 56 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 y = 3 3 257 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 56 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 y = 2 5 257 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 56 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 y = 3 5 257 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 56 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 y = 2 7 257 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 56 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 y = 2 2 263 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 56 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 y = 2 3 263 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 57 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 y = 3 3 263 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 57 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 y = 2 5 263 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 58 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 y = 3 5 263 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 58 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 y = 2 7 263 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 58 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 ...

14   Pass
n = randi(2000)+5; % generate a random integer greater than 5 and smaller than 2006 y = goldbach3(n); assert(isequal(y,sort(y))) assert(all(isprime(y))) assert(sum(y)==n)

x = Columns 1 through 15 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 Columns 16 through 30 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 45 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 Columns 46 through 60 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 75 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 Columns 76 through 90 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 Columns 91 through 105 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 Columns 106 through 120 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 Columns 121 through 135 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 Columns 136 through 150 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 Columns 151 through 165 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 Columns 166 through 180 983 991 997 1009 1013 1019 1021 1031 1033 1039 1049 1051 1061 1063 1069 Columns 181 through 195 1087 1091 1093 1097 1103 1109 1117 1123 1129 1151 1153 1163 1171 1181 1187 Columns 196 through 210 1193 1201 1213 1217 1223 1229 1231 1237 1249 1259 1277 1279 1283 1289 1291 Columns 211 through 225 1297 1301 1303 1307 1319 1321 1327 1361 1367 1373 1381 1399 1409 1423 1427 Columns 226 through 240 1429 1433 1439 1447 1451 1453 1459 1471 1481 1483 1487 1489 1493 1499 1511 Columns 241 through 255 1523 1531 1543 1549 1553 1559 1567 1571 1579 1583 1597 1601 1607 1609 1613 Columns 256 through 266 1619 1621 1627 1637 1657 1663 1667 1669 1693 1697 1699 y = 2 3 1697

15   Pass
valid = zeros(1,50); for k = 1:50 n = randi(1000)+5; % generate a random integer greater than 5 and smaller than 1006 yk = goldbach3(n); valid(k) = (isequal(yk,sort(yk)) & all(isprime(yk)) & sum(yk)==n); end assert(all(valid));

x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 63 283 293 307 y = 2 31 277 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 39 127 131 137 139 149 151 157 163 167 y = 2 3 163 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 77 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 y = 3 3 389 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 90 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 Columns 91 through 120 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 Columns 121 through 127 661 673 677 683 691 701 709 y = 2 3 709 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 62 283 293 y = 3 7 283 x = 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 y = 3 3 97 x = 2 3 5 y = 2 2 2 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 90 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 Columns 91 through 120 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 Columns 121 through 150 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 Column 151 877 y = 2 19 859 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 90 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 Columns 91 through 120 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 Columns 121 through 150 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 Columns 151 through 165 877 881 883 887 907 911 919 929 937 941 947 953 967 971 977 y = 2 5 971 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 90 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 Columns 91 through 120 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 Columns 121 through 150 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 829 839 853 857 859 863 Columns 151 through 163 877 881 883 887 907 911 919 929 937 941 947 953 967 y = 2 13 953 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 77 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 y = 2 2 389 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 68 283 293 307 311 313 317 331 337 y = 3 3 337 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 66 283 293 307 311 313 317 y = 2 2 317 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 90 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 Columns 91 through 120 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 Columns 121 through 124 661 673 677 683 y = 3 3 683 x = Columns 1 through 30 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 101 103 107 109 113 Columns 31 through 60 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 227 229 233 239 241 251 257 263 269 271 277 281 Columns 61 through 90 283 293 307 311 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 419 421 431 433 439 443 449 457 461 463 Columns 91 through 120 467 479 487 491 499 503 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 617 619 631 641 643 647 653 659 Columns 121 through 150 661 673 677 683 691 701 709 719 727 733 739 743 751 757 761 769 773 787 797 809 8...

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