Cody

# Problem 60. The Goldbach Conjecture

Solution 926850

Submitted on 24 Jul 2016 by Martin C.
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### Test Suite

Test Status Code Input and Output
1   Pass
nList = 28:6:76; for i = 1:length(nList) n = nList(i); [p1,p2] = goldbach(n) assert(isprime(p1) && isprime(p2) && (p1+p2==n)); end

p = 2 3 5 7 11 13 17 19 23 difference = 26 25 23 21 17 15 11 9 5 p1 = 23 p2 = 5 p1 = 17 p2 = 11 p1 = 11 p2 = 17 p1 = 5 p2 = 23 p1 = 5 p2 = 23 p = 2 3 5 7 11 13 17 19 23 29 31 difference = 32 31 29 27 23 21 17 15 11 5 3 p1 = 31 p2 = 3 p1 = 29 p2 = 5 p1 = 23 p2 = 11 p1 = 17 p2 = 17 p1 = 11 p2 = 23 p1 = 5 p2 = 29 p1 = 3 p2 = 31 p1 = 3 p2 = 31 p = 2 3 5 7 11 13 17 19 23 29 31 37 difference = 38 37 35 33 29 27 23 21 17 11 9 3 p1 = 37 p2 = 3 p1 = 29 p2 = 11 p1 = 23 p2 = 17 p1 = 17 p2 = 23 p1 = 11 p2 = 29 p1 = 3 p2 = 37 p1 = 3 p2 = 37 p = 2 3 5 7 11 13 17 19 23 29 31 37 41 43 difference = 44 43 41 39 35 33 29 27 23 17 15 9 5 3 p1 = 43 p2 = 3 p1 = 41 p2 = 5 p1 = 29 p2 = 17 p1 = 23 p2 = 23 p1 = 17 p2 = 29 p1 = 5 p2 = 41 p1 = 3 p2 = 43 p1 = 3 p2 = 43 p = 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 difference = 50 49 47 45 41 39 35 33 29 23 21 15 11 9 5 p1 = 47 p2 = 5 p1 = 41 p2 = 11 p1 = 29 p2 = 23 p1 = 23 p2 = 29 p1 = 11 p2 = 41 p1 = 5 p2 = 47 p1 = 5 p2 = 47 p = 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 difference = 56 55 53 51 47 45 41 39 35 29 27 21 17 15 11 5 p1 = 53 p2 = 5 p1 = 47 p2 = 11 p1 = 41 p2 = 17 p1 = 29 p2 = 29 p1 = 17 p2 = 41 p1 = 11 p2 = 47 p1 = 5 p2 = 53 p1 = 5 p2 = 53 p = Columns 1 through 16 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 Columns 17 through 18 59 61 difference = Columns 1 through 16 62 61 59 57 53 51 47 45 41 35 33 27 23 21 17 11 Columns 17 through 18 5 3 p1 = 61 p2 = 3 p1 = 59 p2 = 5 p1 = 53 p2 = 11 p1 = 47 p2 = 17 p1 = 41 p2 = 23 p1 = 23 p2 = 41 p1 = 17 p2 = 47 p1 = 11 p2 = 53 p1 = 5 p2 = 59 p1 = 3 p2 = 61 p1 = 3 p2 = 61 p = Columns 1 through 16 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 Columns 17 through 19 59 61 67 difference = Columns 1 through 16 68 67 65 63 59 57 53 51 47 41 39 33 29 27 23 17 Columns 17 through 19 11 9 3 p1 = 67 p2 = 3 p1 = 59 p2 = 11 p1 = 53 p2 = 17 p1 = 47 p2 = 23 p1 = 41 p2 = 29 p1 = 29 p2 = 41 p1 = 23 p2 = 47 p1 = 17 p2 = 53 p1 = 11 p2 = 59 p1 = 3 p2 = 67 p1 = 3 p2 = 67 p = Columns 1 through 16 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 Columns 17 through 21 59 61 67 71 73 difference = Columns 1 through 16 74 73 71 69 65 63 59 57 53 47 45 39 35 33 29 23 Columns 17 through 21 17 15 9 5 3 p1 = 73 p2 = 3 p1 = 71 p2 = 5 p1 = 59 p2 = 17 p1 = 53 p2 = 23 p1 = 47 p2 = 29 p1 = 29 p2 = 47 p1 = 23 p2 = 53 p1 = 17 p2 = 59 p1 = 5 p2 = 71 p1 = 3 p2 = 73 p1 = 3 p2 = 73

2   Pass
nList = [18 20 22 100 102 114 1000 2000 36 3600]; for i = 1:length(nList) n = nList(i); [p1,p2] = goldbach(n) assert(isprime(p1) && isprime(p2) && (p1+p2==n)); end

p = 2 3 5 7 11 13 17 difference = 16 15 13 11 7 5 1 p1 = 13 p2 = 5 p1 = 11 p2 = 7 p1 = 7 p2 = 11 p1 = 5 p2 = 13 p1 = 5 p2 = 13 p = 2 3 5 7 11 13 17 19 difference = 18 17 15 13 9 7 3 1 p1 = 17 p2 = 3 p1 = 13 p2 = 7 p1 = 7 p2 = 13 p1 = 3 p2 = 17 p1 = 3 p2 = 17 p = 2 3 5 7 11 13 17 19 difference = 20 19 17 15 11 9 5 3 p1 = 19 p2 = 3 p1 = 17 p2 = 5 p1 = 11 p2 = 11 p1 = 5 p2 = 17 p1 = 3 p2 = 19 p1 = 3 p2 = 19 p = Columns 1 through 16 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 Columns 17 through 25 59 61 67 71 73 79 83 89 97 difference = Columns 1 through 16 98 97 95 93 89 87 83 81 77 71 69 63 59 57 53 47 Columns 17 through 25 41 39 33 29 27 21 17 11 3 p1 = 97 p2 = 3 p1 = 89 p2 = 11 p1 = 83 p2 = 17 p1 = 71 p2 = 29 p1 = 59 p2 = 41 p1 = 53 p2 = 47 p1 = 47 p2 = 53 p1 = 41 p2 = 59 p1 = 29 p2 = 71 p1 = 17 p2 = 83 p1 = 11 p2 = 89 p1 = 3 p2 = 97 p1 = 3 p2 = 97 p = Columns 1 through 16 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 Columns 17 through 26 59 61 67 71 73 79 83 89 97 101 difference = Columns 1 through 16 100 99 97 95 91 89 85 83 79 73 71 65 61 59 55 49 Columns 17 through 26 43 41 35 31 29 23 19 13 5 1 p1 = 97 p2 = 5 p1 = 89 p2 = 13 p1 = 83 p2 = 19 p1 = 79 p2 = 23 p1 = 73 p2 = 29 p1 = 71 p2 = 31 p1 = 61 p2 = 41 p1 = 59 p2 = 43 p1 = 43 p2 = 59 p1 = 41 p2 = 61 p1 = 31 p2 = 71 p1 = 29 p2 = 73 p1 = 23 p2 = 79 p1 = 19 p2 = 83 p1 = 13 p2 = 89 p1 = 5 p2 = 97 p1 = 5 p2 = 97 p = Columns 1 through 16 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 Columns 17 through 30 59 61 67 71 73 79 83 89 97 101 103 107 109 113 difference = Columns 1 through 16 112 111 109 107 103 101 97 95 91 85 83 77 73 71 67 61 Columns 17 through 30 55 53 47 43 41 35 31 25 17 13 11 7 5 1 p1 = 109 p2 = 5 p1 = 107 p2 = 7 p1 = 103 p2 = 11 p1 = 101 p2 = 13 p1 = 97 p2 = 17 p1 = 83 p2 = 31 p1 = 73 p2 = 41 p1 = 71 p2 = 43 p1 = 67 p2 = 47 p1 = 61 p2 = 53 p1 = 53 p2 = 61 p1 = 47 p2 = 67 p1 = 43 p2 = 71 p1 = 41 p2 = 73 p1 = 31 p2 = 83 p1 = 17 p2 = 97 p1 = 13 p2 = 101 p1 = 11 p2 = 103 p1 = 7 p2 = 107 p1 = 5 p2 = 109 p1 = 5 p2 = 109 p = Columns 1 through 16 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 Columns 17 through 32 59 61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 Columns 33 through 48 137 139 149 151 157 163 167 173 179 181 191 193 197 199 211 223 Columns 49 through 64 227 229 233 239 241 251 257 263 269 271 277 281 283 293 307 311 Columns 65 through 80 313 317 331 337 347 349 353 359 367 373 379 383 389 397 401 409 Columns 81 through 96 419 421 431 433 439 443 449 457 461 463 467 479 487 491 499 503 Columns 97 through 112 509 521 523 541 547 557 563 569 571 577 587 593 599 601 607 613 Columns 113 through 128 617 619 631 641 643 647 653 659 661 673 677 683 691 701 709 719 Columns 129 through 144 727 733 739 743 751 757 761 769 773 787 797 809 811 821 823 827 Columns 145 through 160 829 839 853 857 859 863 877 881 883 887 907 911 919 929 937 941 Columns 161 through 168 947 953 967 971 977 983 991 997 difference = Columns 1 through 16 998 997 995 993 989 987 983 981 977 971 969 963 959 957 953 947 Columns 17 through 32 941 939 933 929 927 921 917 911 903 899 897 893 891 887 873 869 Columns 33 through 48 863 861 851 849 843 837 833 827 821 819 809 807 803 801 789 777 Columns 49 through 64 773 771 767 761 759 749 743 737 731 729 723 719 717 707 693 689 Columns 65 through 80 687 683 669 663 653 651 647 641 633 627 621 617 611 603 599 591 Columns 81 through 96 581 579 569 567 561 557 551 543 539 537 533 521 513 509 501 497 Columns 97 through 112 491 479 477 459 453 443 437 431 429 423 413 407 401 399 393 387 Columns 113 through 128 383 381 369 359 357 353 347 341 339 327 323 317 309 299 291 281 Columns 129 through 144 273 267 261 257 249 243 239 231 227 213 203 191 189 179 177 173 Columns 145 through 160 171 161 147 143 141 137 123 119 117 113 93 89 81 71 63 59 Columns 161 through 168 53 47 33 29 23 17 9 3 p1 = 997 p2 = 3 p1 = 983 p2 = 17 p1 = 977 p2 = 23 p1 = 971 p2 = 29 p1 = 953 p2 = 47 p1 = 947 p2 = 53 p1 = 941 p2 = 59 p1 = 929 p2 = 71 p1 = 911 p2 = 89 p1 = 887 p2 = 113 p1 = 863 p2 = 137 p1 = 827 p2 = 173 p1 = 821 p2 = 179 p1 = 809 p2 = 191 p1 = 773 p2 = 227 p1 = 761 p2 = 239 p1 = 743 p2 = 257 p1 = 719 p2 = 281 p1 = 683 p2 = 317 p1 = 653 p2 = 347 p1 = 647 p2 = 353 p1 = 641 p2 = 359 p1 = 617 p2 = 383 p1 = 599 p2 = 401 p1 = 569 p2 = 431 p1 = 557 p2 = 443 p1 = 521 p2 = 479 p1 = 509 p2 = 491 p1 = 491 p2 = 509 p1 = 479 p2 = 521 p1 = 443 p2 = 557 p1 = 431 p2 = 569 p1 = 401 p2 = 599 p1 = 383 p2 = 617 p1 = 359 p2 = 641 p1 = 353 p2 = 647 p1 = 347 p2 = 653 p1 = 317 p2 = 683 p1 = 281 p2 = 719 p1 = 257 p2 = 743 p1 = 239 p2 = 761 p1 = 227 p2 = 773 p1 = 191 p2 = 809 p1 = 179 p2 = 821 p1 = 173 p2 = 827 p1 = 137 p2 = 863 p1 = 113 p2 = 887 p1 = 89 p2 = 911 p1 = 71 p2 = 929 p1 = 59 p2 = 941 p1 = 53 p2 = 947 p1 = 47 p2 = 953 p1 = 29 p2 = 971 p1 = 23 p2 = 977 p1 = 17 p2 = 983 p1 = 3 p2 = 997 p1 = 3 p2 = 997 p = Columns 1 through 8 2 3 5 7 11 13 17 19 Columns 9 through 16 23 29 31 37 41 43 47 53 Columns 17 through 24 59 61 67 71 73 79 83 89 Columns 25 through 32 97 101 103 107 109 113 127 131 Columns 33 through 40 137 139 149 151 157 163 167 173 Columns 41 through 48 179 181 191 193 197 199 211 223 Columns 49 through 56 227 229 233 239 241 251 257 263 Columns 57 through 64 269 271 277 281 283 293 307 311 Columns 65 through 72 313 317 331 337 347 349 353 359 Columns 73 through 80 367 373 379 383 389 397 401 409 Columns 81 through 88 419 421 431 433 439 443 449 457 Columns 89 through 96 461 463 467 479 487 491 499 503 Columns 97 through 104 509 521 523 541 547 557 563 569 Columns 105 through 112 571 577 587 593 599 601 607 613 Columns 113 through 120 617 619 631 641 643 647 653 659 Columns 121 through 128 661 673 677 683 ...