Primbixes are primes of the form:
1 + 2 * r * s
Where r, s are primes.
Since r, s are primes, they might also be primbixes, which in turn contains new primes.
The data structure one gets from a primbix this way, is a binary tree.
A primbix value counts the number of leaves in the associated binary tree.
For more information, see Primbix paper.
The minimum primbix sequence is a sequence that contains the smallest natural numbers of increasing primbix values. Due to the difficulty of theorem proving about this sequence, very little is currently known about it.
There is an ongoing effort to search for more terms in the minimum primbix sequence and these are the results so far:
0: 0
2: 1
13: 2
53: 3
317: 4
3407: 5
8243: 6
49459: 7
197837: 8
1187023: 9
18314419: 10
112006043: 11
491325707: 12
2047857083: 13
9869296583: 14
107478087043: 15
107478087043 was found 13.06.2025 19:13 UTC.
The minimum primbix with value 16 is above 156 000 000 000 and less or equal to 460 785 710 279 (which has primbix value 16).
If you are interested in helping to reduce this bound, then you can take a look at this example code.
There are currently 16 dedicated CPU cores that work on this search 24/7.
To make collaboration easier, the search is split into billions, with the highest minimum primbix found so far in this range:
[0, 1 000 000 000): 12, 491 325 707 (done)
[1 000 000 000, 2 000 000 000): 12, 1 027 760 099 (done)
[2 000 000 000, 3 000 000 000): 13, 2 047 857 083 (done)
[3 000 000 000, 4 000 000 000): 13, 3 410 832 779 (done)
[4 000 000 000, 5 000 000 000): 13, 4 671 906 587 (done)
[5 000 000 000, 6 000 000 000): 12, 5 093 513 903 (done)
[6 000 000 000, 7 000 000 000): 13, 6 379 061 603 (done)
[7 000 000 000, 8 000 000 000): 13, 7 696 274 087 (done)
[8 000 000 000, 9 000 000 000): 13, 8 412 786 287 (done)
[9 000 000 000, 10 000 000 000): 14, 9 869 296 583 (done)
[10 000 000 000, 11 000 000 000): 13, 10 089 537 083 (done)
[11 000 000 000, 12 000 000 000): 13, 11 046 928 547 (done)
[12 000 000 000, 13 000 000 000): 13, 12 239 338 733 (done)
[13 000 000 000, 14 000 000 000): 13, 13 259 283 623 (done)
[14 000 000 000, 15 000 000 000): 13, 14 584 191 563 (done)
[15 000 000 000, 16 000 000 000): 13, 15 008 809 763 (done)
[16 000 000 000, 17 000 000 000): 13, 16 001 431 163 (done)
[17 000 000 000, 18 000 000 000): 14, 17 913 014 507 (done)
[18 000 000 000, 19 000 000 000): 12, 18 099 433 019 (done)
[19 000 000 000, 20 000 000 000): 13, 19 523 734 163 (done)
[20 000 000 000, 21 000 000 000): 14, 20 221 905 659 (done)
[21 000 000 000, 22 000 000 000): 13, 21 063 309 803 (done)
[22 000 000 000, 23 000 000 000): 13, 22 610 227 247 (done)
[23 000 000 000, 24 000 000 000): 13, 23 460 041 299 (done)
[24 000 000 000, 25 000 000 000): 14, 24 270 247 487 (done)
[25 000 000 000, 26 000 000 000): 13, 25 048 480 819 (done)
[26 000 000 000, 27 000 000 000): 14, 26 311 925 327 (done)
[27 000 000 000, 28 000 000 000): 13, 27 487 985 267 (done)
[28 000 000 000, 29 000 000 000): 14, 28 031 439 523 (done)
[29 000 000 000, 30 000 000 000): 14, 29 582 478 467 (done)
[30 000 000 000, 31 000 000 000): 12, 30 093 953 423 (done)
[31 000 000 000, 32 000 000 000): 13, 31 195 729 667 (done)
[32 000 000 000, 33 000 000 000): 13, 32 255 212 643 (done)
[33 000 000 000, 34 000 000 000): 13, 33 047 302 427 (done)
[34 000 000 000, 35 000 080 000): 13, 34 140 614 999 (done)
[35 000 000 000, 36 000 000 000): 13, 35 208 863 003 (done)
[36 000 000 000, 37 000 000 000): 13, 36 409 064 987 (done)
[37 000 000 000, 38 000 000 000): 13, 37 211 568 323 (done)
[38 000 000 000, 39 000 000 000): 13, 38 158 619 903 (done)
[39 000 000 000, 40 000 000 000): 13, 39 637 041 707 (done)
[40 000 000 000, 41 000 000 000): 13, 40 095 103 943 (done)
[41 000 000 000, 42 000 000 000): 13, 41 448 637 739 (done)
[42 000 000 000, 43 000 000 000): 12, 42 181 308 083 (done)
[43 000 000 000, 44 000 000 000): 13, 43 985 953 763 (done)
[44 000 000 000, 45 000 000 000): 13, 44 037 007 667 (done)
[45 000 000 000, 46 000 000 000): 12, 45 018 664 253 (done)
[46 000 000 000, 47 000 000 000): 14, 46 850 738 027 (done)
[47 000 000 000, 48 000 000 000): 13, 47 033 867 723 (done)
[48 000 000 000, 49 000 000 000): 13, 48 658 282 187 (done)
[49 000 000 000, 50 000 000 000): 13, 49 021 505 459 (done)
[50 000 000 000, 51 000 000 000): 14, 50 593 408 883 (done)
[51 000 000 000, 52 000 000 000): 13, 51 568 193 639 (done)
[52 000 000 000, 53 000 000 000): 13, 52 082 576 867 (done)
[53 000 000 000, 54 000 000 000): 13, 53 152 075 343 (done)
[54 000 000 000, 55 000 000 000): 13, 54 047 183 899 (done)
[55 000 000 000, 56 000 000 000): 13, 55 026 244 187 (done)
[56 000 000 000, 57 000 000 000): 13, 56 147 597 147 (done)
[57 000 000 000, 58 000 000 000): 13, 57 088 349 387 (done)
[58 000 000 000, 59 000 000 000): 14, 58 868 152 667 (done)
[59 000 000 000, 60 000 000 000): 13, 59 228 779 067 (done)
[60 000 000 000, 61 000 000 000): 13, 60 152 410 523 (done)
[61 000 000 000, 62 000 000 000): 14, 61 189 469 203 (done)
[62 000 000 000, 63 000 000 000): 13, 62 127 795 263 (done)
[63 000 000 000, 64 000 000 000): 14, 63 298 441 103 (done)
[64 000 000 000, 65 000 000 000): 14, 64 068 721 103 (done)
[65 000 000 000, 66 000 000 000): 14, 65 858 650 787 (done)
[66 000 000 000, 67 000 000 000): 14, 66 203 883 203 (done)
[67 000 000 000, 68 000 000 000): 14, 67 123 528 523 (done)
[68 000 000 000, 69 000 000 000): 14, 68 912 114 963 (done)
[69 000 000 000, 70 000 000 000): 14, 69 091 969 307 (done)
[70 000 000 000, 71 000 000 000): 14, 70 990 350 323 (done)
[71 000 000 000, 72 000 000 000): 13, 71 313 184 379 (done)
[72 000 000 000, 73 000 000 000): 13, 72 242 159 723 (done)
[73 000 000 000, 74 000 000 000): 14, 73 195 221 503 (done)
[74 000 000 000, 75 000 000 000): 14, 74 283 398 879 (done)
[75 000 000 000, 76 000 000 000): 13, 75 399 157 403 (done)
[76 000 000 000, 77 000 000 000): 13, 76 030 752 719 (done)
[77 000 000 000, 78 000 000 000): 13, 77 291 624 843 (done)
[78 000 000 000, 79 000 000 000): 13, 78 605 486 423 (done)
[79 000 000 000, 80 000 000 000): 13, 79 034 299 307 (done)
[80 000 000 000, 81 000 000 000): 13, 80 184 069 863 (done)
[81 000 000 000, 82 000 000 000): 13, 81 101 693 579 (done)
[82 000 000 000, 83 000 000 000): 13, 82 415 464 819 (done)
[83 000 000 000, 84 000 000 000): 13, 83 530 471 373 (done)
[84 000 000 000, 85 000 000 000): 13, 84 123 658 643 (done)
[85 000 000 000, 86 000 000 000): 13, 85 315 438 739 (done)
[86 000 000 000, 87 000 000 000): 14, 86 024 144 483 (done)
[87 000 000 000, 88 000 000 000): 13, 87 160 741 979 (done)
[88 000 000 000, 89 000 000 000): 13, 88 391 170 619 (done)
[89 000 000 000, 90 000 000 000): 13, 89 448 484 991 (done)
[90 000 000 000, 91 000 000 000): 12, 90 000 568 499 (done)
[91 000 000 000, 92 000 000 000): 13, 91 008 196 427 (done)
[92 000 000 000, 93 000 000 000): 13, 92 168 614 739 (done)
[93 000 000 000, 94 000 000 000): 13, 93 175 427 339 (done)
[94 000 000 000, 95 000 000 000): 14, 94 503 472 643 (done)
[95 000 000 000, 96 000 000 000): 13, 95 004 006 827 (done)
[96 000 000 000, 97 000 000 000): 14, 96 207 537 467 (done)
[97 000 000 000, 98 000 000 000): 12, 97 000 717 939 (done)
[98 000 000 000, 99 000 000 000): 14, 98 861 233 763 (done)
[99 000 000 000, 100 000 000 000): 14, 99 474 595 139 (done)
[100 000 000 000, 101 000 000 000): 13, 100 779 916 607 (done)
[101 000 000 000, 102 000 000 000): 12, 101 069 289 779 (done)
[102 000 000 000, 103 000 000 000): 14, 102 837 801 203 (done)
[103 000 000 000, 104 000 000 000): 13, 103 052 992 403 (done)
[104 000 000 000, 105 000 000 000): 13, 104 130 780 827 (done)
[105 000 000 000, 106 000 000 000): 13, 105 164 674 403 (done)
[106 000 000 000, 107 000 000 000): 13, 106 222 789 787 (done)
[107 000 000 000, 108 000 000 000): 15, 107 478 087 043 (done)
[108 000 000 000, 109 000 000 000): 14, 108 543 457 739 (done)
[109 000 000 000, 110 000 000 000): 13, 109 199 494 003 (done)
[110 000 000 000, 111 000 000 000): 12, 110 357 057 963 (done)
[111 000 000 000, 112 000 000 000): 14, 111 202 867 439 (done)
[112 000 000 000, 113 000 000 000): 13, 112 063 189 247 (done)
[113 000 000 000, 114 000 000 000): 13, 113 170 332 323 (done)
[114 000 000 000, 115 000 000 000): 13, 114 360 384 683 (done)
[115 000 000 000, 116 000 000 000): 13, 115 299 191 299 (done)
[116 000 000 000, 117 000 000 000): 13, 116 197 766 963 (done)
[117 000 000 000, 118 000 000 000): 13, 117 157 815 443 (done)
[118 000 000 000, 119 000 000 000): 14, 118 026 292 427 (done)
[119 000 000 000, 120 000 000 000): 13, 119 991 406 979 (done)
[120 000 000 000, 121 000 000 000): 13, 120 142 740 779 (done)
[121 000 000 000, 122 000 000 000): 14, 121 876 669 979 (done)
[122 000 000 000, 123 000 000 000): 13, 122 089 346 783 (done)
[123 000 000 000, 124 000 000 000): 13, 123 088 754 939 (done)
[124 000 000 000, 125 000 000 000): 13, 124 177 173 647 (done)
[125 000 000 000, 126 000 000 000): 13, 125 107 159 643 (done)
[126 000 000 000, 127 000 000 000): 14, 126 301 533 539 (done)
[127 000 000 000, 128 000 000 000): 13, 127 124 714 867 (done)
[128 000 000 000, 129 000 000 000): 13, 128 602 257 383 (done)
[129 000 000 000, 130 000 000 000): 14, 129 642 090 563 (done)
[130 000 000 000, 131 000 000 000): 14, 130 392 831 083 (done)
[131 000 000 000, 132 000 000 000): 14, 131 080 792 187 (done)
[132 000 000 000, 133 000 000 000): 13, 132 454 408 259 (done)
[133 000 000 000, 134 000 000 000): 13, 133 043 218 019 (done)
[134 000 000 000, 135 000 000 000): 13, 134 237 440 619 (done)
[135 000 000 000, 136 000 000 000): 13, 135 248 281 667 (done)
[136 000 000 000, 137 000 000 000): 13, 136 039 074 803 (done)
[137 000 000 000, 138 000 000 000): 14, 137 719 853 267 (done)
[138 000 000 000, 139 000 000 000): 13, 138 105 132 443 (done)
[139 000 000 000, 140 000 000 000): 13, 139 266 250 859 (done)
[140 000 000 000, 141 000 000 000): 13, 140 104 159 067 (done)
[141 000 000 000, 142 000 000 000): 14, 141 945 809 003 (done)
[142 000 000 000, 143 000 000 000): 14, 142 752 559 163 (done)
[143 000 000 000, 144 000 000 000): 13, 143 768 837 579 (done)
[144 000 000 000, 145 000 000 000): 13, 144 131 193 587 (done)
[145 000 000 000, 146 000 000 000): 14, 145 588 871 147 (done)
[146 000 000 000, 147 000 000 000): 14, 146 701 576 367 (done)
[147 000 000 000, 148 000 000 000): 13, 147 632 734 763 (done)
[148 000 000 000, 149 000 000 000): 13, 148 078 709 039 (done)
[149 000 000 000, 150 000 000 000): 13, 149 391 592 643 (done)
[150 000 000 000, 151 000 000 000): 13, 150 263 805 059 (done)
[151 000 000 000, 152 000 000 000): 14, 151 995 614 339 (done)
[152 000 000 000, 153 000 000 000): 12, 152 026 136 519 (done)
[153 000 000 000, 154 000 000 000): 12, 153 259 000 283 (done)
[154 000 000 000, 155 000 000 000): 14, 154 865 725 739 (done)
[155 000 000 000, 156 000 000 000): 13, 155 199 473 699 (done)
[156 000 000 000, 157 000 000 000): <--- 8 CPUs
[174 000 000 000, 175 000 000 000): 13, 174 007 028 003 (done)
[175 000 000 000, 176 000 000 000): 14, 175 898 379 947 (done)
[176 000 000 000, 177 000 000 000): 15, 176 115 709 139 (done)
[300 000 000 000, 301 000 000 000): 13, 300 128 528 243 (done)
[301 000 000 000, 302 000 000 000): 13, 301 073 167 403 (done)
[302 000 000 000, 303 000 000 000): 13, 302 091 778 223 (done)
[303 000 000 000, 304 000 000 000): 14, 303 773 952 739 (done)
[304 000 000 000, 305 000 000 000): 14, 304 350 398 699 (done)
[305 000 000 000, 306 000 000 000): 14, 305 623 136 867 (done)
[306 000 000 000, 307 000 000 000): 13, 306 088 216 403 (done)
[307 000 000 000, 308 000 000 000): <--- 8 CPUs
[455 000 000 000, 456 000 000 000): 13, 455 041 432 883 (done)
[456 000 000 000, 457 000 000 000): 14, 456 286 740 179 (done)
[457 000 000 000, 458 000 000 000): 13, 457 109 239 283 (done)
[458 000 000 000, 459 000 000 000): 14, 458 353 629 827 (done)
[459 000 000 000, 460 000 000 000): 14, 459 492 057 587 (done)
[460 000 000 000, 461 000 000 000): 16, 460 785 710 279 (done)
Primbixes have ideal properties for communication between two advanced civilization at galactic scale. This is because it is a simple definition that might be discovered independently by two advanced civilizations without previously being in contact. Sharing primbixes might be a way to establish common ground under first contact, plus that the interest to keep in touch, despite other difficulties of getting in contact such as extreme large distances, can be kept up by collaboration on primbix research.
Primes have fascinated mathematicians for over 2 millenia. However, with the invention of computers, primes are no longer as exciting they once appeared to be. Both efficient algorithms and theoretical advancements means we know a lot more about primes now than in the past.
Primbixes increases the difficulty compared to primes, in a way where the advantage of computers can be balanced with human intuition and creativity. A new discovery by a supercomputer can be used in combination with human knowledge that can compete with each other using secrets.
This way, primbixes are designed to let people become engaged as a hobby, in addition to expert researchers working in this field to advance human knowledge.