On Tuesday, 4 February 2025 at 17:17:42 UTC, Jabari Zakiya wrote:
> On Monday, 3 February 2025 at 04:59:43 UTC, monkyyy wrote:
> On Monday, 3 February 2025 at 04:15:09 UTC, Jabari Zakiya wrote:
> I translated this Ruby code:
FYI.
This code finds all the prime pairs that sum to n for all even integers n > 2.
It (Ruby code) is included in a paper I just released (Feb 2, 2025) on Goldbach's Conjecture (1742) and Bertrand's Postulate (1845). For those interested in Prime|Number Theory check it out. A lot of new, good, stuff is in it!
Proof of Goldbach's Conjecture and Bertrand's Postulate Using Prime Generator Theory (PGT)
https://www.academia.edu/127404211/Proof_of_Goldbachs_Conjecture_and_Bertrands_Postulate_Using_Prime_Generator_Theory_PGT_
I updated the code to make entering data easier.
It now mimics the Ruby|Crystal code and takes "humanized" data strings.
You can now run the code as: $ ./primes_pair_lohi_u32 123_456_780
I also created two versions, one for u32 input values, and one for u64.
Unless you have lots of memmory, the u32 version is best to use.
Here's the u32 input size version.
// Compile with ldc2: $ ldc2 --release -O3 -mcpu native prime_pairs_lohi_u32.d
// Run as: $ ./prime_pairs_lohi_u32 123_456_780
module prime_pairs;
import std;
import std.datetime.stopwatch : StopWatch;
void prime_pairs_lohi(uint n) { // inputs can be of size u32
if ((n&1) == 1 || n < 4) { return writeln("Input not even n > 2"); }
if (n <= 6) { writeln([n, 1]); writeln([n/2, n/2]); writeln([n/2, n/2]); return; }
// generate the low-half-residues (lhr) r < n/2
auto ndiv2 = n/2; // llr:hhr midpoint
auto rhi = n-2; // max residue limit
uint[] lhr = iota(3, ndiv2, 2).filter!(e => gcd(e, n) == 1).array;
// store all the powers of the lhr members < n-2
uint[] lhr_mults; // for lhr values not part of a pcp
foreach(r; lhr) { // step thru the lhr members
auto r_pwr = r; // set to first power of r
if (r > rhi/r_pwr) break; // exit if r^2 > n-2, as all others are too
while (r < rhi/r_pwr) // while r^e < n-2
lhr_mults ~=(r_pwr *= r); // store its current power of rA
}
// store all the cross-products of the lhr members < n-2
foreach(i, r; lhr) {
auto ri_max = rhi / r; // ri can't multiply r with values > this
if (lhr[i+1] > ri_max) break; // exit if product of consecutive r’s > n-2
foreach(ri; lhr[i+1..$]) { // for each residue in reduced list
if (ri > ri_max) break; // exit for r if cross-product with ri > n-2
lhr_mults ~= r * ri; // store value if < n-2
} }
// convert lhr_mults vals > n/2 to their lhr complements n-r,
// store them, those < n/2, in lhr_del; it now holds non-pcp lhr vals
auto lhr_del = lhr_mults.map!((r_del) => r_del > ndiv2 ? n - r_del : r_del).array;
lhr_del.sort!("a < b");
lhr = setDifference(lhr, lhr_del).array;
writeln([n, lhr.length]); // show n and pcp prime pairs count
writeln([lhr[0], n-lhr[0]]); // show first pcp prime pair of n
writeln([lhr[$-1],n-lhr[$-1]]); // show last pcp prime pair of n
}
void main(string[] args) { // directly recieve input from terminal
string[] inputs = args[1..$]; // can include '_': 123_456
auto nums = inputs.map!(i => i.filter!(n => n != '_'));
auto n = nums.map!(f => f.to!uint())[0];
auto timer = StopWatch(); // create execution timer
timer.start(); // start it
prime_pairs_lohi(n); // run routine
writeln(timer.peek()); // show timer results
}
Here's the u64 version.
// Compile with ldc2: $ ldc2 --release -O3 -mcpu native prime_pairs_lohi_u64.d
// Run as: $ ./prime_pairs_lohi_u64 123_456_780
module prime_pairs;
import std;
import std.datetime.stopwatch : StopWatch;
void prime_pairs_lohi(ulong n) { // inputs can be of size u64
if ((n&1) == 1 || n < 4) { return writeln("Input not even n > 2"); }
if (n <= 6) { writeln([n, 1]); writeln([n/2, n/2]); writeln([n/2, n/2]); return; }
// generate the low-half-residues (lhr) r < n/2
auto ndiv2 = n/2; // llr:hhr midpoint
auto rhi = n-2; // max residue limit
ulong[] lhr = iota(3, ndiv2, 2).filter!(e => gcd(e, n) == 1).array;
// store all the powers of the lhr members < n-2
ulong[] lhr_mults; // for lhr values not part of a pcp
foreach(r; lhr) { // step thru the lhr members
auto r_pwr = r; // set to first power of r
if (r > rhi/r_pwr) break; // exit if r^2 > n-2, as all others are too
while (r < rhi/r_pwr) // while r^e < n-2
lhr_mults ~=(r_pwr *= r); // store its current power of rA
}
// store all the cross-products of the lhr members < n-2
foreach(i, r; lhr) {
auto ri_max = rhi / r; // ri can't multiply r with values > this
if (lhr[i+1] > ri_max) break; // exit if product of consecutive r’s > n-2
foreach(ri; lhr[i+1..$]) { // for each residue in reduced list
if (ri > ri_max) break; // exit for r if cross-product with ri > n-2
lhr_mults ~= r * ri; // store value if < n-2
} }
// convert lhr_mults vals > n/2 to their lhr complements n-r,
// store them, those < n/2, in lhr_del; it now holds non-pcp lhr vals
auto lhr_del = lhr_mults.map!((r_del) => r_del > ndiv2 ? n - r_del : r_del).array;
lhr_del.sort!("a < b");
lhr = setDifference(lhr, lhr_del).array;
writeln([n, lhr.length]); // show n and pcp prime pairs count
writeln([lhr[0], n-lhr[0]]); // show first pcp prime pair of n
writeln([lhr[$-1],n-lhr[$-1]]); // show last pcp prime pair of n
}
void main(string[] args) { // directly recieve input from terminal
string[] inputs = args[1..$]; // can include '_': 123_456
auto nums = inputs.map!(i => i.filter!(n => n != '_'));
auto n = nums.map!(f => f.to!ulong())[0];
auto timer = StopWatch(); // create execution timer
timer.start(); // start it
prime_pairs_lohi(n); // run routine
writeln(timer.peek()); // show timer results
}