| Pattern d: d = 0, 2, 6, 8, 12 | ||||||
|
Gap end merit = 10.1317949 •∫dt / log5 t Gap start |
||||||
| Rank | Gap Size | Gap start | Next Prime Quintuplet | Merit | Who | When |
|---|---|---|---|---|---|---|
| 1 | 6 | 5 | 11 | 2.014091 | Alexei Kourbatov | 2013 |
| 2 | 90 | 11 | 101 | 1.615652 | Alexei Kourbatov | 2013 |
| 3 | 1 380 | 101 | 1 481 | 1.475054 | Alexei Kourbatov | 2013 |
| 4 | 14 580 | 1 481 | 16 061 | 2.821400 | Alexei Kourbatov | 2013 |
| 5 | 21 510 | 22 271 | 43 781 | 1.812143 | Alexei Kourbatov | 2013 |
| 6 | 88 830 | 55 331 | 144 161 | 4.561779 | Alexei Kourbatov | 2013 |
| 7 | 97 020 | 536 441 | 633 461 | 2.382030 | Alexei Kourbatov | 2013 |
| 8 | 107 100 | 661 091 | 768 191 | 2.439605 | Alexei Kourbatov | 2013 |
| 9 | 112 140 | 1 461 401 | 1 573 541 | 1.945726 | Alexei Kourbatov | 2013 |
| 10 | 301 890 | 1 615 841 | 1 917 731 | 4.969311 | Alexei Kourbatov | 2013 |
| 11 | 401 820 | 5 527 001 | 5 928 821 | 4.462615 | Alexei Kourbatov | 2013 |
| 12 | 577 710 | 11 086 841 | 11 664 551 | 5.170724 | Alexei Kourbatov | 2013 |
| 13 | 689 850 | 35 240 321 | 35 930 171 | 4.398101 | Alexei Kourbatov | 2013 |
| 14 | 846 210 | 53 266 391 | 54 112 601 | 4.799780 | Alexei Kourbatov | 2013 |
| 15 | 857 010 | 72 610 121 | 73 467 131 | 4.461704 | Alexei Kourbatov | 2013 |
| 16 | 986 160 | 92 202 821 | 93 188 981 | 4.809118 | Alexei Kourbatov | 2013 |
| 17 | 1 655 130 | 117 458 981 | 119 114 111 | 7.555860 | Alexei Kourbatov | 2013 |
| 18 | 2 035 740 | 196 091 171 | 198 126 911 | 8.115696 | Alexei Kourbatov | 2013 |
| 19 | 2 266 320 | 636 118 781 | 638 385 101 | 6.705826 | Alexei Kourbatov | 2013 |
| 20 | 2 467 290 | 975 348 161 | 977 815 451 | 6.578094 | Alexei Kourbatov | 2013 |
| 21 | 2 614 710 | 1 156 096 301 | 1 158 711 011 | 6.691992 | Alexei Kourbatov | 2013 |
| 22 | 3 305 310 | 1 277 816 921 | 1 281 122 231 | 8.259169 | Alexei Kourbatov | 2013 |
| 23 | 3 530 220 | 1 347 962 381 | 1 351 492 601 | 8.709581 | Alexei Kourbatov | 2013 |
| 24 | 3 880 050 | 2 195 593 481 | 2 199 473 531 | 8.536129 | Alexei Kourbatov | 2013 |
| 25 | 3 885 420 | 3 128 295 551 | 3 132 180 971 | 7.878418 | Alexei Kourbatov | 2013 |
| 26 | 5 290 440 | 4 015 046 591 | 4 020 337 031 | 10.13547 | Alexei Kourbatov | 2013 |
| 27 | 5 713 800 | 8 280 668 651 | 8 286 382 451 | 9.318915 | Alexei Kourbatov | 2013 |
| 28 | 6 049 890 | 9 027 127 091 | 9 033 176 981 | 9.682722 | Alexei Kourbatov | 2013 |
| 29 | 6 128 340 | 15 686 967 971 | 15 693 096 311 | 8.707265 | Alexei Kourbatov | 2013 |
| 30 | 7 949 040 | 18 901 038 971 | 18 908 988 011 | 10.85626 | Alexei Kourbatov | 2013 |
| 31 | 7 971 270 | 21 785 624 291 | 21 793 595 561 | 10.56575 | Alexei Kourbatov | 2013 |
| 32 | 10 770 150 | 30 310 287 431 | 30 321 057 581 | 13.32532 | Alexei Kourbatov | 2013 |
| 33 | 11 340 840 | 107 604 759 671 | 107 616 100 511 | 10.86452 | Alexei Kourbatov | 2013 |
| 34 | 12 249 510 | 140 760 439 991 | 140 772 689 501 | 11.13382 | Alexei Kourbatov | 2013 |
| 35 | 12 413 190 | 162 661 360 481 | 162 673 773 671 | 10.97012 | Alexei Kourbatov | 2013 |
| 36 | 14 181 000 | 187 735 329 491 | 187 749 510 491 | 12.19014 | Alexei Kourbatov | 2013 |
| 37 | 16 092 930 | 327 978 626 531 | 327 994 719 461 | 12.43832 | Alexei Kourbatov | 2013 |
| 38 | 16 360 350 | 508 259 311 991 | 508 275 672 341 | 11.65040 | Alexei Kourbatov | 2013 |
| 39 | 16 756 740 | 620 537 349 191 | 620 554 105 931 | 11.50052 | Alexei Kourbatov | 2013 |
| 40 | 16 981 320 | 667 672 901 711 | 667 689 883 031 | 11.49880 | Alexei Kourbatov | 2013 |
| 41 | 17 590 230 | 1 079 628 551 621 | 1 079 646 141 851 | 10.91339 | Alexei Kourbatov | 2013 |
| 42 | 19 285 140 | 1 104 604 933 841 | 1 104 624 218 981 | 11.91569 | Alexei Kourbatov | 2013 |
| 43 | 19 525 590 | 1 182 148 717 481 | 1 182 168 243 071 | 11.91775 | Alexei Kourbatov | 2013 |
| 44 | 22 230 180 | 1 197 151 034 531 | 1 197 173 264 711 | 13.53780 | Alexei Kourbatov | 2013 |
| 45 | 22 549 470 | 2 286 697 462 781 | 2 286 720 012 251 | 12.24026 | Alexei Kourbatov | 2013 |
| 46 | 29 986 530 | 2 435 950 632 251 | 2 435 980 618 781 | 16.09760 | Alexei Kourbatov | 2013 |
| 47 | 32 168 520 | 3 276 773 115 431 | 3 276 805 283 951 | 16.39860 | Alexei Kourbatov | 2013 |
| 48 | 36 392 070 | 5 229 301 162 991 | 5 229 337 555 061 | 17.11766 | Alexei Kourbatov | 2013 |
| 49 | 38 695 230 | 9 196 865 051 651 | 9 196 903 746 881 | 16.54361 | Alexei Kourbatov | 2013 |
| 50 | 40 156 200 | 14 660 925 945 221 | 14 660 966 101 421 | 15.88783 | Alexei Kourbatov | 2013 |
| 51 | 40 618 500 | 21 006 417 451 961 | 21 006 458 070 461 | 15.15051 | Alexei Kourbatov | 2013 |
| 52 | 40 996 500 | 22 175 175 736 991 | 22 175 216 733 491 | 15.15726 | Alexei Kourbatov | 2013 |
| 53 | 41 452 320 | 22 726 966 063 091 | 22 727 007 515 411 | 15.26464 | Alexei Kourbatov | 2013 |
| 54 | 47 578 140 | 22 931 291 089 451 | 22 931 338 667 591 | 17.49498 | Alexei Kourbatov | 2013 |
| 55 | 48 630 870 | 31 060 723 328 351 | 31 060 771 959 221 | 17.02567 | Alexei Kourbatov | 2013 |
| 56 | 55 044 570 | 85 489 258 071 311 | 85 489 313 115 881 | 16.41605 | Alexei Kourbatov | 2013 |
| 57 | 58 465 680 | 90 913 430 825 291 | 90 913 489 290 971 | 17.27011 | Alexei Kourbatov | 2013 |
| 58 | 65 048 220 | 96 730 325 054 171 | 96 730 390 102 391 | 19.03021 | Alexei Kourbatov | 2013 |
| 59 | 65 737 980 | 199 672 700 175 071 | 199 672 765 913 051 | 17.20662 | Alexei Kourbatov | 2013 |
| 60 | 70 788 900 | 275 444 947 505 591 | 275 445 018 294 491 | 17.64948 | Alexei Kourbatov | 2013 |
| 61 | 73 970 820 | 331 992 774 272 981 | 331 992 848 243 801 | 17.93356 | Alexei Kourbatov | 2013 |
| 62 | 79 985 130 | 465 968 834 865 971 | 465 968 914 851 101 | 18.43783 | Alexei Kourbatov | 2013 |
| 63 | 82 420 290 | 686 535 413 263 871 | 686 535 495 684 161 | 17.94572 | Alexei Kourbatov | 2013 |
| 64 | 88 092 570 | 761 914 822 198 961 | 761 914 910 291 531 | 18.89097 | Alexei Kourbatov | 2013 |
| 65 | 89 780 040 | 1 144 708 485 094 541 | 1 144 708 574 874 581 | 18.14893 | Norman Luhn | 11 Nov 2022 |
| 66 | 89 999 700 | 1 151 759 067 731 681 | 1 151 759 157 731 381 | 18.17723 | Norman Luhn | 11 Nov 2022 |
| 67 | 92 278 290 | 1 652 750 938 094 561 | 1 652 751 030 372 851 | 17.69660 | Norman Luhn | 11 Nov 2022 |
| 68 | 96 260 340 | 2 738 101 496 927 891 | 2 738 101 593 188 231 | 17.18611 | Norman Luhn | 11 Nov 2022 |
| 69 | 106 240 140 | 2 783 651 538 720 581 | 2 783 651 644 960 721 | 18.92392 | Norman Luhn | 11 Nov 2022 |
| 70 | 109 965 150 | 2 791 544 717 194 061 | 2 791 544 827 159 211 | 19.57964 | Norman Luhn | 11 Nov 2022 |
| 71 | 113 717 100 | 3 943 459 477 670 891 | 3 943 459 591 387 991 | 19.29233 | Norman Luhn | 12 Nov 2022 |
| 72 | 125 811 090 | 4 323 771 559 383 161 | 4 323 771 685 194 251 | 21.07258 | Norman Luhn | 12 Nov 2022 |
| 73 | 131 738 370 | 6 044 436 969 077 321 | 6 044 437 100 815 691 | 21.06681 | Norman Luhn | 13 Nov 2022 |
| 74 | 139 529 370 | 10 562 580 060 974 231 | 10 562 580 200 503 601 | 20.67522 | Karl Desfontaines | 09 Mar 2026 |
| 75 | 168 027 810 | 15 133 721 677 503 041 | 15 133 721 845 530 851 | 23.71941 | Karl Desfontaines | 09 Mar 2026 |
| 76 | 178 760 820 | 34 920 923 430 856 361 | 34 920 923 609 617 181 | 22.58383 | Karl Desfontaines | 09 Mar 2026 |
| 77 | 184 218 210 | 46 079 131 386 176 171 | 46 079 131 570 394 381 | 22.44444 | Karl Desfontaines | 09 Mar 2026 |
| 78 | 184 785 600 | 57 346 824 898 620 611 | 57 346 825 083 406 211 | 21.88261 | Karl Desfontaines | 09 Mar 2026 |
| 79 | 192 796 260 | 58 253 947 071 177 491 | 58 253 947 263 973 751 | 22.78487 | Karl Desfontaines | 09 Mar 2026 |
| 80 | 193 892 790 | 83 532 388 376 128 451 | 83 532 388 570 021 241 | 21.87408 | Karl Desfontaines | 09 Mar 2026 |
| 81 | 196 884 660 | 97 986 508 761 097 211 | 97 986 508 957 981 871 | 21.76225 | Karl Desfontaines | 09 Mar 2026 |
| 82 | 201 522 810 | 111 065 711 778 130 001 | 111 065 711 979 652 811 | 21.92165 | Karl Desfontaines | 09 Mar 2026 |
| 83 | 201 834 990 | 129 290 949 243 309 851 | 129 290 949 445 144 841 | 21.53552 | Karl Desfontaines | 09 Mar 2026 |
| 84 | 205 634 220 | 138 530 650 788 966 341 | 138 530 650 994 600 561 | 21.74971 | Karl Desfontaines | 09 Mar 2026 |
| 85 | 205 639 020 | 164 615 366 554 024 691 | 164 615 366 759 663 711 | 21.28104 | Karl Desfontaines | 09 Mar 2026 |
| 86 | 209 310 030 | 211 640 197 495 983 071 | 211 640 197 705 293 101 | 20.98731 | Karl Desfontaines | 11 Mar 2026 |
| 87 | 210 390 180 | 212 593 384 912 337 831 | 212 593 385 122 728 011 | 21.08374 | Karl Desfontaines | 11 Mar 2026 |
| 88 | 246 422 820 | 212 794 130 699 505 071 | 212 794 130 945 927 891 | 24.69174 | Karl Desfontaines | 11 Mar 2026 |
| 89 | 260 469 510 | 304 417 398 744 969 941 | 304 417 399 005 439 451 | 24.95897 | Karl Desfontaines | 11 Mar 2026 |
| 90 | 263 436 900 | 506 905 017 188 344 121 | 506 905 017 451 781 021 | 23.70358 | Karl Desfontaines | 15 Mar 2026 |
| 91 | 270 831 540 | 778 254 413 408 249 411 | 778 254 413 679 080 951 | 23.12700 | Karl Desfontaines | 21 Mar 2026 |
| 92 | 271 974 450 | 902 844 165 279 667 601 | 902 844 165 551 642 051 | 22.81050 | Karl Desfontaines | 22 Mar 2026 |
| 93 | 272 379 990 | 957 147 552 513 005 591 | 957 147 552 785 385 581 | 22.68384 | Karl Desfontaines | 23 Mar 2026 |
| 94 | 287 431 320 | 1 014 411 058 324 368 071 | 1 014 411 058 611 799 391 | 23.77004 | Karl Desfontaines | 24 Mar 2026 |
| 95 | 293 912 970 | 1 441 096 608 815 670 341 | 1 441 096 609 109 583 311 | 23.30257 | Karl Desfontaines | 28 Mar 2026 |
| 96 | 294 856 590 | 1 486 821 848 856 342 071 | 1 486 821 849 151 198 661 | 23.29025 | Karl Desfontaines | 29 Mar 2026 |
| 97 | 297 727 080 | 1 526 568 758 830 411 181 | 1 526 568 759 128 138 261 | 23.44299 | Karl Desfontaines | 29 Mar 2026 |
| 98 | 328 465 500 | 1 734 416 380 092 856 541 | 1 734 416 380 421 322 041 | 25.47266 | Karl Desfontaines | 31 Mar 2026 |
| 99 | 336 185 640 | 2 078 425 428 527 525 711 | 2 078 425 428 863 711 351 | 25.51692 | Karl Desfontaines | 04 Apr 2026 |
| 100 | 339 899 070 | 2 112 734 195 451 751 841 | 2 112 734 195 791 650 911 | 25.74874 | Karl Desfontaines | 04 Apr 2026 |
| 101 | 344 524 950 | 3 489 588 853 793 469 101 | 3 489 588 854 137 994 051 | 24.60113 | Karl Desfontaines | 19 Apr 2026 |
| 102 | 414 129 540 | 4 169 073 028 882 213 211 | 4 169 073 029 296 342 751 | 28.96284 | Karl Desfontaines | 23 Apr 2026 |
| 103 | 443 796 990 | 11 196 162 955 723 583 681 | 11 196 162 956 167 380 671 | 27.69641 | Karl Desfontaines | 06 Jun 2026 |
| 104 | 458 085 060 | 14 903 182 045 215 932 591 | 14 903 182 045 674 017 651 | 27.67401 | Karl Desfontaines | 21 Jun 2026 |
| Maximal gaps below 1.75 · 1019 | ||||||
| Pattern d: d = 0, 4, 6, 10, 12 | ||||||
|
Gap end merit = 10.1317949 •∫dt / log5 t Gap start |
||||||
| Rank | Gap Size | Gap start | Next Prime Quintuplet | Merit | Who | When |
|---|---|---|---|---|---|---|
| 1 | 90 | 7 | 97 | 2.447286 | Alexei Kourbatov | 2013 |
| 2 | 1 770 | 97 | 1 867 | 1.668845 | Alexei Kourbatov | 2013 |
| 3 | 2 190 | 3 457 | 5 647 | 0.528546 | Alexei Kourbatov | 2013 |
| 4 | 10 080 | 5 647 | 15 727 | 1.541767 | Alexei Kourbatov | 2013 |
| 5 | 24 360 | 19 417 | 43 777 | 2.109313 | Alexei Kourbatov | 2013 |
| 6 | 35 910 | 43 777 | 79 687 | 2.250890 | Alexei Kourbatov | 2013 |
| 7 | 156 750 | 101 107 | 257 857 | 6.260574 | Alexei Kourbatov | 2013 |
| 8 | 208 620 | 1 621 717 | 1 830 337 | 3.460981 | Alexei Kourbatov | 2013 |
| 9 | 304 920 | 3 690 517 | 3 995 437 | 3.856354 | Alexei Kourbatov | 2013 |
| 10 | 306 390 | 5 425 747 | 5 732 137 | 3.431607 | Alexei Kourbatov | 2013 |
| 11 | 328 020 | 8 799 607 | 9 127 627 | 3.160959 | Alexei Kourbatov | 2013 |
| 12 | 422 190 | 9 511 417 | 9 933 607 | 3.966749 | Alexei Kourbatov | 2013 |
| 13 | 526 350 | 16 388 917 | 16 915 267 | 4.195292 | Alexei Kourbatov | 2013 |
| 14 | 639 330 | 22 678 417 | 23 317 747 | 4.628609 | Alexei Kourbatov | 2013 |
| 15 | 706 860 | 31 875 577 | 32 582 437 | 4.637159 | Alexei Kourbatov | 2013 |
| 16 | 866 460 | 37 162 117 | 38 028 577 | 5.437616 | Alexei Kourbatov | 2013 |
| 17 | 1 030 770 | 64 210 117 | 65 240 887 | 5.549032 | Alexei Kourbatov | 2013 |
| 18 | 1 111 620 | 119 732 017 | 120 843 637 | 5.051827 | Alexei Kourbatov | 2013 |
| 19 | 1 147 440 | 200 271 517 | 201 418 957 | 4.551967 | Alexei Kourbatov | 2013 |
| 20 | 1 151 100 | 203 169 007 | 204 320 107 | 4.549408 | Alexei Kourbatov | 2013 |
| 21 | 1 447 530 | 241 307 107 | 242 754 637 | 5.470321 | Alexei Kourbatov | 2013 |
| 22 | 1 769 670 | 342 235 627 | 344 005 297 | 6.114615 | Alexei Kourbatov | 2013 |
| 23 | 1 793 070 | 367 358 347 | 369 151 417 | 6.085234 | Alexei Kourbatov | 2013 |
| 24 | 2 024 610 | 378 200 227 | 380 224 837 | 6.820180 | Alexei Kourbatov | 2013 |
| 25 | 2 320 170 | 438 140 947 | 440 461 117 | 7.531215 | Alexei Kourbatov | 2013 |
| 26 | 2 335 080 | 446 609 407 | 448 944 487 | 7.543325 | Alexei Kourbatov | 2013 |
| 27 | 2 403 570 | 711 616 897 | 714 020 467 | 6.918590 | Alexei Kourbatov | 2013 |
| 28 | 3 558 030 | 966 813 007 | 970 371 037 | 9.504986 | Alexei Kourbatov | 2013 |
| 29 | 4 195 500 | 2 044 014 607 | 2 048 210 107 | 9.384831 | Alexei Kourbatov | 2013 |
| 30 | 4 463 130 | 3 510 456 787 | 3 514 919 917 | 8.815000 | Alexei Kourbatov | 2013 |
| 31 | 4 602 360 | 4 700 738 167 | 4 705 340 527 | 8.509854 | Alexei Kourbatov | 2013 |
| 32 | 5 210 190 | 5 798 359 657 | 5 803 569 847 | 9.192503 | Alexei Kourbatov | 2013 |
| 33 | 5 331 060 | 7 896 734 467 | 7 902 065 527 | 8.785638 | Alexei Kourbatov | 2013 |
| 34 | 5 368 530 | 12 654 304 207 | 12 659 672 737 | 7.986482 | Alexei Kourbatov | 2013 |
| 35 | 5 546 520 | 13 890 542 377 | 13 896 088 897 | 8.087940 | Alexei Kourbatov | 2013 |
| 36 | 5 966 220 | 14 662 830 817 | 14 668 797 037 | 8.599857 | Alexei Kourbatov | 2013 |
| 37 | 6 557 670 | 15 434 185 927 | 15 440 743 597 | 9.349536 | Alexei Kourbatov | 2013 |
| 38 | 6 590 640 | 17 375 054 227 | 17 381 644 867 | 9.162921 | Alexei Kourbatov | 2013 |
| 39 | 7 359 450 | 17 537 596 327 | 17 544 955 777 | 10.21156 | Alexei Kourbatov | 2013 |
| 40 | 8 673 840 | 25 988 605 537 | 25 997 279 377 | 11.08034 | Alexei Kourbatov | 2013 |
| 41 | 9 334 500 | 66 407 160 637 | 66 416 495 137 | 9.842651 | Alexei Kourbatov | 2013 |
| 42 | 9 570 330 | 74 862 035 617 | 74 871 605 947 | 9.852137 | Alexei Kourbatov | 2013 |
| 43 | 12 983 670 | 77 710 388 047 | 77 723 371 717 | 13.26671 | Alexei Kourbatov | 2013 |
| 44 | 14 597 820 | 144 124 106 167 | 144 138 703 987 | 13.20737 | Alexei Kourbatov | 2013 |
| 45 | 16 396 710 | 210 222 262 087 | 210 238 658 797 | 13.79162 | Alexei Kourbatov | 2013 |
| 46 | 17 639 070 | 585 234 882 097 | 585 252 521 167 | 12.23750 | Alexei Kourbatov | 2013 |
| 47 | 18 803 070 | 926 017 532 047 | 926 036 335 117 | 11.99440 | Alexei Kourbatov | 2013 |
| 48 | 23 392 830 | 986 089 952 917 | 986 113 345 747 | 14.75314 | Alexei Kourbatov | 2013 |
| 49 | 24 122 280 | 2 819 808 136 417 | 2 819 832 258 697 | 12.62237 | Alexei Kourbatov | 2013 |
| 50 | 26 753 370 | 3 013 422 626 107 | 3 013 449 379 477 | 13.83811 | Alexei Kourbatov | 2013 |
| 51 | 26 870 130 | 3 538 026 326 827 | 3 538 053 196 957 | 13.51678 | Alexei Kourbatov | 2013 |
| 52 | 27 378 120 | 4 674 635 167 747 | 4 674 662 545 867 | 13.12718 | Alexei Kourbatov | 2013 |
| 53 | 28 837 200 | 5 757 142 722 757 | 5 757 171 559 957 | 13.34358 | Alexei Kourbatov | 2013 |
| 54 | 30 726 150 | 7 464 931 087 717 | 7 464 961 813 867 | 13.60544 | Alexei Kourbatov | 2013 |
| 55 | 33 297 270 | 8 402 871 269 197 | 8 402 904 566 467 | 14.45306 | Alexei Kourbatov | 2013 |
| 56 | 33 489 540 | 9 292 699 799 017 | 9 292 733 288 557 | 14.29316 | Alexei Kourbatov | 2013 |
| 57 | 33 619 740 | 10 985 205 390 997 | 10 985 239 010 737 | 13.95339 | Alexei Kourbatov | 2013 |
| 58 | 36 586 110 | 12 992 848 206 847 | 12 992 884 792 957 | 14.76716 | Alexei Kourbatov | 2013 |
| 59 | 42 483 960 | 15 589 051 692 667 | 15 589 094 176 627 | 16.63967 | Alexei Kourbatov | 2013 |
| 60 | 44 167 530 | 24 096 376 903 597 | 24 096 421 071 127 | 16.11067 | Alexei Kourbatov | 2013 |
| 61 | 44 771 370 | 37 371 241 083 097 | 37 371 285 854 467 | 15.21609 | Alexei Kourbatov | 2013 |
| 62 | 58 972 920 | 38 728 669 335 607 | 38 728 728 308 527 | 19.92864 | Alexei Kourbatov | 2013 |
| 63 | 67 170 090 | 91 572 717 670 537 | 91 572 784 840 627 | 19.81901 | Alexei Kourbatov | 2013 |
| 64 | 69 538 470 | 109 950 817 237 357 | 109 950 886 775 827 | 19.94399 | Alexei Kourbatov | 2013 |
| 65 | 72 542 190 | 325 554 440 818 297 | 325 554 513 360 487 | 17.63879 | Alexei Kourbatov | 2013 |
| 66 | 73 032 960 | 481 567 288 596 127 | 481 567 361 629 087 | 16.75342 | Alexei Kourbatov | 2013 |
| 67 | 74 101 230 | 501 796 510 663 237 | 501 796 584 764 467 | 16.89541 | Alexei Kourbatov | 2013 |
| 68 | 76 243 980 | 535 243 109 721 577 | 535 243 185 965 557 | 17.21921 | Alexei Kourbatov | 2013 |
| 69 | 78 597 210 | 657 351 798 174 427 | 657 351 876 771 637 | 17.22252 | Alexei Kourbatov | 2013 |
| 70 | 86 266 530 | 818 872 754 682 547 | 818 872 840 949 077 | 18.30600 | Alexei Kourbatov | 2013 |
| 71 | 107 597 490 | 991 851 356 676 277 | 991 851 464 273 767 | 22.20589 | Alexei Kourbatov | 2013 |
| 72 | 120 049 440 | 3 273 959 015 090 497 | 3 273 959 135 139 937 | 20.90253 | Richard Fischer | 06 Nov 2025 |
| 73 | 128 737 680 | 5 471 423 048 269 687 | 5 471 423 177 007 367 | 20.87142 | Richard Fischer | 06 Nov 2025 |
| 74 | 187 387 410 | 8 689 385 372 669 707 | 8 689 385 560 057 117 | 28.51310 | Richard Fischer | 06 Nov 2025 |
| 75 | 192 395 160 | 136 637 864 734 087 807 | 136 637 864 926 482 967 | 20.38493 | Karl Desfontaines | 09 Mar 2026 |
| 76 | 197 028 300 | 137 222 733 747 737 167 | 137 222 733 944 765 467 | 20.86453 | Karl Desfontaines | 09 Mar 2026 |
| 77 | 201 134 940 | 145 597 946 191 524 637 | 145 597 946 392 659 577 | 21.14024 | Karl Desfontaines | 09 Mar 2026 |
| 78 | 213 183 600 | 151 470 643 612 971 037 | 151 470 643 826 154 637 | 22.29484 | Karl Desfontaines | 09 Mar 2026 |
| 79 | 218 805 390 | 212 803 971 604 289 827 | 212 803 971 823 095 217 | 21.92433 | Karl Desfontaines | 11 Mar 2026 |
| 80 | 251 436 990 | 263 538 397 276 778 707 | 263 538 397 528 215 697 | 24.52964 | Karl Desfontaines | 11 Mar 2026 |
| 81 | 264 227 040 | 458 177 602 344 466 387 | 458 177 602 608 693 427 | 24.07158 | Karl Desfontaines | 20 Mar 2026 |
| 82 | 282 291 450 | 685 306 719 459 193 207 | 685 306 719 741 484 657 | 24.48118 | Karl Desfontaines | 20 Mar 2026 |
| 83 | 290 722 950 | 1 052 606 552 700 172 357 | 1 052 606 552 990 895 307 | 23.93538 | Karl Desfontaines | 25 Mar 2026 |
| 84 | 291 196 830 | 1 062 235 601 016 860 107 | 1 062 235 601 308 056 937 | 23.94810 | Karl Desfontaines | 25 Mar 2026 |
| 85 | 295 573 230 | 1 522 571 371 276 960 177 | 1 522 571 371 572 533 407 | 23.28069 | Karl Desfontaines | 29 Mar 2026 |
| 86 | 321 617 940 | 1 692 263 728 668 493 147 | 1 692 263 728 990 111 087 | 25.01480 | Karl Desfontaines | 31 Mar 2026 |
| 87 | 339 435 180 | 2 575 076 310 525 043 597 | 2 575 076 310 864 478 777 | 25.11902 | Karl Desfontaines | 07 Apr 2026 |
| 88 | 346 089 870 | 2 880 314 446 040 917 927 | 2 880 314 446 387 007 797 | 25.27576 | Karl Desfontaines | 16 Apr 2026 |
| 89 | 437 682 000 | 3 799 045 318 466 500 177 | 3 799 045 318 904 182 177 | 30.94398 | Karl Desfontaines | 21 Apr 2026 |
| 90 | 441 651 000 | 17 508 095 904 586 071 217 | 17 508 095 905 027 722 217 | 26.19970 | Karl Desfontaines | 04 Jul 2026 |
| Maximal gaps below 1.75 · 1019 | ||||||
|
Gap end merit = 20.2635899 •∫dt / log5 t Gap start |
||||||
| Rank | Gap Size | Gap start | Next Prime Quintuplet | Merit | Who | When |
|---|---|---|---|---|---|---|
| 1 | 2 | 5 | 7 | 2.325345 | Norman Luhn | 17 Jan 2023 |
| 2 | 4 | 7 | 11 | 1.702838 | Norman Luhn | 17 Jan 2023 |
| 3 | 86 | 11 | 97 | 3.191734 | Norman Luhn | 17 Jan 2023 |
| 4 | 1 380 | 101 | 1 481 | 2.950108 | Norman Luhn | 17 Jan 2023 |
| 5 | 1 590 | 1 867 | 3 457 | 1.074268 | Norman Luhn | 17 Jan 2023 |
| 6 | 2 190 | 3 457 | 5 647 | 1.057092 | Norman Luhn | 17 Jan 2023 |
| 7 | 10 080 | 5 647 | 15 727 | 3.083535 | Norman Luhn | 17 Jan 2023 |
| 8 | 21 506 | 22 271 | 43 777 | 3.623705 | Norman Luhn | 17 Jan 2023 |
| 9 | 24 356 | 55 331 | 79 687 | 2.913718 | Norman Luhn | 17 Jan 2023 |
| 10 | 43 054 | 101 107 | 144 161 | 3.963805 | Norman Luhn | 17 Jan 2023 |
| 11 | 48 724 | 470 077 | 518 801 | 2.548873 | Norman Luhn | 17 Jan 2023 |
| 12 | 90 176 | 536 441 | 626 617 | 4.437438 | Norman Luhn | 17 Jan 2023 |
| 13 | 208 620 | 1 621 717 | 1 830 337 | 6.921963 | Norman Luhn | 17 Jan 2023 |
| 14 | 296 520 | 9 627 461 | 9 923 981 | 5.562460 | Norman Luhn | 17 Jan 2023 |
| 15 | 403 530 | 17 958 757 | 18 362 287 | 6.267510 | Norman Luhn | 17 Jan 2023 |
| 16 | 415 594 | 37 162 117 | 37 577 711 | 5.225229 | Norman Luhn | 17 Jan 2023 |
| 17 | 449 104 | 49 682 617 | 50 131 721 | 5.200557 | Norman Luhn | 17 Jan 2023 |
| 18 | 680 524 | 53 432 077 | 54 112 601 | 7.716635 | Norman Luhn | 17 Jan 2023 |
| 19 | 818 580 | 134 702 797 | 135 521 377 | 7.212090 | Norman Luhn | 17 Jan 2023 |
| 20 | 937 024 | 197 189 887 | 198 126 911 | 7.465643 | Norman Luhn | 17 Jan 2023 |
| 21 | 976 170 | 373 604 711 | 374 580 881 | 6.599401 | Norman Luhn | 17 Jan 2023 |
| 22 | 977 970 | 493 287 161 | 494 265 131 | 6.165704 | Norman Luhn | 17 Jan 2023 |
| 23 | 1 034 284 | 637 350 817 | 638 385 101 | 6.119238 | Norman Luhn | 17 Jan 2023 |
| 24 | 1 091 670 | 712 555 001 | 713 646 671 | 6.284055 | Norman Luhn | 17 Jan 2023 |
| 25 | 1 359 544 | 860 705 887 | 862 065 431 | 7.473265 | Norman Luhn | 17 Jan 2023 |
| 26 | 1 395 450 | 1 009 180 807 | 1 010 576 257 | 7.380909 | Norman Luhn | 17 Jan 2023 |
| 27 | 1 626 454 | 1 157 084 557 | 1 158 711 011 | 8.324521 | Norman Luhn | 17 Jan 2023 |
| 28 | 1 924 226 | 1 389 333 221 | 1 391 257 447 | 9.428118 | Norman Luhn | 17 Jan 2023 |
| 29 | 2 203 860 | 3 194 724 097 | 3 196 927 957 | 8.895217 | Norman Luhn | 17 Jan 2023 |
| 30 | 2 354 396 | 4 380 061 991 | 4 382 416 387 | 8.846522 | Norman Luhn | 17 Jan 2023 |
| 31 | 2 934 034 | 6 265 437 247 | 6 268 371 281 | 10.17714 | Norman Luhn | 17 Jan 2023 |
| 32 | 3 405 240 | 8 716 936 927 | 8 720 342 167 | 10.98387 | Norman Luhn | 17 Jan 2023 |
| 33 | 4 144 050 | 9 027 682 837 | 9 031 826 887 | 13.26505 | Norman Luhn | 17 Jan 2023 |
| 34 | 4 612 650 | 25 746 845 471 | 25 751 458 121 | 11.80798 | Norman Luhn | 17 Jan 2023 |
| 35 | 4 694 040 | 27 095 815 927 | 27 100 509 967 | 11.88916 | Norman Luhn | 17 Jan 2023 |
| 36 | 4 770 026 | 57 004 580 441 | 57 009 350 467 | 10.37335 | Norman Luhn | 17 Jan 2023 |
| 37 | 6 252 450 | 64 749 989 531 | 64 756 241 981 | 13.25276 | Norman Luhn | 17 Jan 2023 |
| 38 | 6 281 974 | 125 461 072 567 | 125 467 354 541 | 11.67908 | Norman Luhn | 17 Jan 2023 |
| 39 | 6 671 400 | 140 763 439 507 | 140 770 110 907 | 12.12753 | Norman Luhn | 17 Jan 2023 |
| 40 | 6 745 830 | 217 403 883 371 | 217 410 629 201 | 11.27535 | Norman Luhn | 17 Jan 2023 |
| 41 | 6 969 390 | 219 466 456 207 | 219 473 425 597 | 11.62797 | Norman Luhn | 17 Jan 2023 |
| 42 | 7 032 810 | 254 585 915 951 | 254 592 948 761 | 11.40592 | Norman Luhn | 17 Jan 2023 |
| 43 | 7 697 040 | 259 545 134 411 | 259 552 831 451 | 12.43742 | Norman Luhn | 17 Jan 2023 |
| 44 | 8 009 910 | 267 613 646 467 | 267 621 656 377 | 12.86786 | Norman Luhn | 17 Jan 2023 |
| 45 | 8 632 800 | 323 447 704 751 | 323 456 337 551 | 13.37977 | Norman Luhn | 17 Jan 2023 |
| 46 | 9 352 856 | 416 795 008 571 | 416 804 361 427 | 13.82181 | Norman Luhn | 17 Jan 2023 |
| 47 | 11 596 620 | 496 350 264 491 | 496 361 861 111 | 16.58902 | Norman Luhn | 17 Jan 2023 |
| 48 | 12 356 190 | 1 722 002 217 907 | 1 722 014 574 097 | 14.10324 | Norman Luhn | 17 Jan 2023 |
| 49 | 12 414 146 | 2 247 007 282 901 | 2 247 019 697 047 | 13.51878 | Norman Luhn | 17 Jan 2023 |
| 50 | 12 635 700 | 2 440 461 612 221 | 2 440 474 247 921 | 13.56199 | Norman Luhn | 17 Jan 2023 |
| 51 | 12 828 270 | 2 817 723 775 117 | 2 817 736 603 387 | 13.42693 | Norman Luhn | 17 Jan 2023 |
| 52 | 14 258 580 | 3 099 650 725 597 | 3 099 664 984 177 | 14.67822 | Norman Luhn | 17 Jan 2023 |
| 53 | 14 490 626 | 3 302 152 083 611 | 3 302 166 574 237 | 14.75407 | Norman Luhn | 17 Jan 2023 |
| 54 | 15 047 344 | 3 590 553 662 947 | 3 590 568 710 291 | 15.10031 | Norman Luhn | 17 Jan 2023 |
| 55 | 18 575 340 | 3 971 417 681 677 | 3 971 436 257 017 | 18.31907 | Norman Luhn | 17 Jan 2023 |
| 56 | 19 136 966 | 11 271 950 385 581 | 11 271 969 522 547 | 15.81706 | Norman Luhn | 17 Jan 2023 |
| 57 | 20 070 120 | 11 626 054 158 281 | 11 626 074 228 401 | 16.50322 | Norman Luhn | 17 Jan 2023 |
| 58 | 21 305 516 | 13 968 495 046 601 | 13 968 516 352 117 | 16.99426 | Norman Luhn | 17 Jan 2023 |
| 59 | 24 819 274 | 15 722 575 542 757 | 15 722 600 362 031 | 19.41463 | Norman Luhn | 17 Jan 2023 |
| 60 | 26 535 600 | 55 267 748 077 897 | 55 267 774 613 497 | 16.94894 | Norman Luhn | 17 Jan 2023 |
| 61 | 26 692 380 | 88 322 991 138 457 | 88 323 017 830 837 | 15.84038 | Karl Desfontaines | 04 Apr 2026 |
| 62 | 26 866 860 | 101 916 005 765 921 | 101 916 032 632 781 | 15.59324 | Norman Luhn | 19 Jan 2023 |
| 63 | 26 963 876 | 120 618 225 533 411 | 120 618 252 497 287 | 15.24716 | Norman Luhn | 19 Jan 2023 |
| 64 | 28 451 606 | 120 632 651 965 361 | 120 632 680 416 967 | 16.08812 | Norman Luhn | 19 Jan 2023 |
| 65 | 28 761 814 | 139 357 211 063 167 | 139 357 239 824 981 | 15.90644 | Norman Luhn | 19 Jan 2023 |
| 66 | 29 069 246 | 146 710 464 482 501 | 146 710 493 551 747 | 15.95015 | Norman Luhn | 19 Jan 2023 |
| 67 | 29 348 460 | 152 377 895 932 391 | 152 377 925 280 851 | 16.01012 | Norman Luhn | 19 Jan 2023 |
| 68 | 31 270 804 | 153 561 290 445 457 | 153 561 321 716 261 | 17.03860 | Norman Luhn | 19 Jan 2023 |
| 69 | 32 676 720 | 174 263 039 990 857 | 174 263 072 667 577 | 17.46395 | Norman Luhn | 19 Jan 2023 |
| 70 | 34 005 810 | 193 262 636 332 387 | 193 262 670 338 197 | 17.89020 | Norman Luhn | 19 Jan 2023 |
| 71 | 39 872 876 | 239 249 216 549 501 | 239 249 256 422 377 | 20.30928 | Norman Luhn | 19 Jan 2023 |
| 72 | 40 033 140 | 414 088 181 123 621 | 414 088 221 156 761 | 18.78246 | Norman Luhn | 19 Jan 2023 |
| 73 | 46 997 490 | 555 818 816 805 607 | 555 818 863 803 097 | 21.11050 | Norman Luhn | 19 Jan 2023 |
| 74 | 52 505 970 | 932 750 269 787 377 | 932 750 322 293 347 | 21.86612 | Norman Luhn | 20 Jan 2023 |
| 75 | 55 578 270 | 2 387 035 579 027 271 | 2 387 035 634 605 541 | 20.23316 | Martin Raab | 27 Jun 2024 |
| 76 | 57 377 426 | 3 107 921 965 038 041 | 3 107 922 022 415 467 | 20.12684 | Martin Raab | 27 Jun 2024 |
| 77 | 57 555 120 | 3 680 960 120 895 971 | 3 680 960 178 451 091 | 19.71706 | Martin Raab | 27 Jun 2024 |
| 78 | 59 647 770 | 3 828 912 282 657 101 | 3 828 912 342 304 871 | 20.32199 | Martin Raab | 27 Jun 2024 |
| 79 | 60 854 970 | 6 109 601 787 913 361 | 6 109 601 848 768 331 | 19.43443 | Martin Raab | 27 Jun 2024 |
| 80 | 65 703 330 | 6 761 179 964 758 357 | 6 761 180 030 461 687 | 20.69272 | Martin Raab | 27 Jun 2024 |
| 81 | 67 654 736 | 8 051 857 534 505 501 | 8 051 857 602 160 237 | 20.80393 | Martin Raab | 27 Jun 2024 |
| 82 | 71 062 444 | 10 551 780 030 699 067 | 10 551 780 101 761 511 | 21.06274 | Karl Desfontaines | 08 Apr 2026 |
| 83 | 72 731 190 | 16 833 793 425 825 281 | 16 833 793 498 556 471 | 20.24310 | Karl Desfontaines | 08 Apr 2026 |
| 84 | 80 996 580 | 16 973 786 085 682 837 | 16 973 786 166 679 417 | 22.51861 | Karl Desfontaines | 08 Apr 2026 |
| 85 | 83 407 796 | 19 287 556 049 478 251 | 19 287 556 132 886 047 | 22.79653 | Karl Desfontaines | 08 Apr 2026 |
| 86 | 86 576 194 | 36 783 587 848 515 247 | 36 783 587 935 091 441 | 21.72669 | Karl Desfontaines | 08 Apr 2026 |
| 87 | 93 776 344 | 41 595 387 947 165 947 | 41 595 388 040 942 291 | 23.15799 | Karl Desfontaines | 09 Apr 2026 |
| 88 | 94 708 020 | 59 224 051 939 010 677 | 59 224 052 033 718 697 | 22.33757 | Karl Desfontaines | 09 Apr 2026 |
| 89 | 101 304 874 | 81 832 217 300 462 767 | 81 832 217 401 767 641 | 22.91790 | Karl Desfontaines | 09 Apr 2026 |
| 90 | 102 239 674 | 128 245 661 829 623 077 | 128 245 661 931 862 751 | 21.84016 | Karl Desfontaines | 09 Apr 2026 |
| 91 | 114 322 020 | 136 219 991 476 487 917 | 136 219 991 590 809 937 | 24.23503 | Karl Desfontaines | 09 Apr 2026 |
| 92 | 117 993 364 | 161 840 270 160 210 787 | 161 840 270 278 204 151 | 24.47408 | Karl Desfontaines | 09 Apr 2026 |
| 93 | 126 472 710 | 288 026 052 662 052 697 | 288 026 052 788 525 407 | 24.40531 | Karl Desfontaines | 10 Apr 2026 |
| 94 | 127 685 756 | 418 877 568 516 088 391 | 418 877 568 643 774 147 | 23.52305 | Karl Desfontaines | 11 Apr 2026 |
| 95 | 129 453 484 | 449 738 380 840 517 767 | 449 738 380 969 971 251 | 23.64090 | Karl Desfontaines | 11 Apr 2026 |
| 96 | 136 249 800 | 455 079 891 101 874 757 | 455 079 891 238 124 557 | 24.84594 | Karl Desfontaines | 11 Apr 2026 |
| 97 | 136 803 660 | 492 901 767 676 749 787 | 492 901 767 813 553 447 | 24.70345 | Karl Desfontaines | 11 Apr 2026 |
| 98 | 152 036 464 | 704 844 397 823 034 187 | 704 844 397 975 070 651 | 26.28007 | Karl Desfontaines | 12 Apr 2026 |
| 99 | 159 887 314 | 1 057 615 185 229 829 917 | 1 057 615 185 389 717 231 | 26.31216 | Karl Desfontaines | 14 Apr 2026 |
| 100 | 169 046 850 | 1 173 996 712 488 490 147 | 1 173 996 712 657 536 997 | 27.47225 | Karl Desfontaines | 25 Mar 2026 |
| 101 | 170 904 090 | 2 699 925 052 192 800 071 | 2 699 925 052 363 704 161 | 25.15385 | Karl Desfontaines | 08 Apr 2026 |
| 102 | 173 380 620 | 2 833 987 826 986 809 791 | 2 833 987 827 160 190 411 | 25.37315 | Karl Desfontaines | 15 Apr 2026 |
| 103 | 182 907 184 | 2 890 418 886 641 820 637 | 2 890 418 886 824 727 821 | 26.70528 | Karl Desfontaines | 16 Apr 2026 |
| 104 | 194 497 800 | 4 038 232 443 548 798 347 | 4 038 232 443 743 296 147 | 27.30645 | Karl Desfontaines | 22 Apr 2026 |
| 105 | 213 907 046 | 5 941 888 873 370 621 531 | 5 941 888 873 584 528 577 | 28.71360 | Karl Desfontaines | 03 May 2026 |
| 106 | 219 058 350 | 8 139 930 897 465 086 767 | 8 139 930 897 684 145 117 | 28.35756 | Karl Desfontaines | 15 May 2026 |
| 107 | 221 820 896 | 9 457 102 073 651 556 341 | 9 457 102 073 873 377 237 | 28.22570 | Karl Desfontaines | 27 May 2026 |
| 108 | 233 995 736 | 12 336 099 814 577 867 681 | 12 336 099 814 811 863 417 | 28.88566 | Karl Desfontaines | 29 May 2026 |
| Maximal gaps below 1.75 · 1019 | ||||||