Triangle Of The Gods

November 10, 2015

The nth element of the Smarandache consecutive number sequence (A007908) is the sequence of the numbers from 1 to n concatenated in order:

1, 12, 123, 1234, 12345, 123456, 1234567, 12345678, 123456789, 12345678910, 1234567891011, 123456789101112, …

The sequence is sometimes called the “Triangle of the Gods,” and the story goes that anyone who can specify the smallest prime number in the sequence is admitted to heaven.

Your task is to find the smallest prime number in the sequence. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

Pages: 1 2

4 Responses to “Triangle Of The Gods”

  1. Francesco said

    Ok, I’ll be the first one to admit I got trolled :P

    Sequence generator:

    q :: [Integer]
    q = map (read . concatMap show . enumFromTo 1) [1..]
    
  2. FA said

    Scala:
    1. stream of Smarandache numbers
    2. stream of primes
    3. take te common elements

      def sqrt(number: BigInt) = {
        val one = BigInt(1)
        def next(n: BigInt, i: BigInt): BigInt = (n + i / n) >> 1
        var n = one
        var n1 = next(n, number)
        while ((n1 - n).abs > one) {
          n = n1
          n1 = next(n, number)
        }
        while (n1 * n1 > number) { n1 -= one }
        n1
      }                                               //> sqrt: (number: BigInt)BigInt
    
      def smarandacheBI(n: BigInt = 1): Stream[BigInt] = {
        if (n % 2 == 0 || n % 5 == 0) smarandacheBI(n + 1) else {
          val akt = (for (s <- BigInt(1) to n) yield s.toString()).reduce(_ + _)
          if(akt.map(_.toInt).sum % 3==0) smarandacheBI(n + 1)
          else {
          println(akt)
          Stream.cons(BigInt(akt), smarandacheBI(n + BigInt(1)))
          }
        }
      }                                               //> smarandacheBI: (n: BigInt)Stream[BigInt]
    
      def isPrimeBI(n: BigInt, d: BigInt = BigInt(2)): Boolean = {
        //println(n+" "+d)
        if (n == 1) false
        else if (d >= sqrt(n)) true
        else if (n % d == 0) false
        else isPrimeBI(n, d + 1)
      }                                               //> isPrimeBI: (n: BigInt, d: BigInt)Boolean
    
      smarandacheBI().filter(isPrimeBI(_)).take(1).toList
    
  3. programmingpraxis said

    Actually, I’ve had more fun factoring elements of the Smarandache sequence than searching for primes:

    >>> while True:
    ...     print
    ...     print "Smarandache", i
    ...     print factors(n, 1, 5)
    ...     i = i + 1
    ...     n = n * 10 ** (ilog(10,i)+1) + i
    ...
    
    Smarandache 1
    [1]
    
    Smarandache 2
    Factoring 2-digit number
    Wheel factors with B=1000: 2, 2, 3; remaining cofactor has 1 digits
    [2, 2, 3]
    
    Smarandache 3
    Factoring 3-digit number
    Wheel factors with B=1000: 3, 41; remaining cofactor has 1 digits
    [3, 41]
    
    Smarandache 4
    Factoring 4-digit number
    Wheel factors with B=1000: 2, 617; remaining cofactor has 1 digits
    [2, 617]
    
    Smarandache 5
    Factoring 5-digit number
    Wheel factors with B=1000: 3, 5, 823; remaining cofactor has 1 digits
    [3, 5, 823]
    
    Smarandache 6
    Factoring 6-digit number
    Wheel factors with B=1000: 2, 2, 2, 2, 2, 2, 3, 643; remaining cofactor has 1 digits
    [2, 2, 2, 2, 2, 2, 3, 643]
    
    Smarandache 7
    Factoring 7-digit number
    Wheel factors with B=1000: 127, 9721; remaining cofactor has 1 digits
    [127, 9721]
    
    Smarandache 8
    Factoring 8-digit number
    Wheel factors with B=1000: 2, 3, 3, 47, 14593; remaining cofactor has 1 digits
    [2, 3, 3, 47, 14593]
    
    Smarandache 9
    Factoring 9-digit number
    Wheel factors with B=1000: 3, 3; remaining cofactor has 8 digits
    Rho found 4-digit factor 3607 with B=100000, remaining cofactor has 4 digits
    Remaining 4-digit cofactor 3803 is prime
    [3, 3, 3607L, 3803L]
    
    Smarandache 10
    Factoring 11-digit number
    Wheel factors with B=1000: 2, 5; remaining cofactor has 10 digits
    Remaining 10-digit cofactor 1234567891 is prime
    [2, 5, 1234567891L]
    
    Smarandache 11
    Factoring 13-digit number
    Wheel factors with B=1000: 3, 7, 13, 67, 107, 630803; remaining cofactor has 1 digits
    [3, 7, 13, 67, 107, 630803L]
    
    Smarandache 12
    Factoring 15-digit number
    Wheel factors with B=1000: 2, 2, 2, 3; remaining cofactor has 13 digits
    Rho found 4-digit factor 2437 with B=100000, remaining cofactor has 10 digits
    Remaining 10-digit cofactor 2110805449 is prime
    [2, 2, 2, 3, 2437L, 2110805449L]
    
    Smarandache 13
    Factoring 17-digit number
    Wheel factors with B=1000: 113; remaining cofactor has 15 digits
    Rho found 6-digit factor 125693 with B=100000, remaining cofactor has 9 digits
    Remaining 9-digit cofactor 869211457 is prime
    [113, 125693L, 869211457L]
    
    Smarandache 14
    Factoring 19-digit number
    Wheel factors with B=1000: 2, 3; remaining cofactor has 18 digits
    Remaining 18-digit cofactor 205761315168520219 is prime
    [2, 3, 205761315168520219L]
    
    Smarandache 15
    Factoring 21-digit number
    Wheel factors with B=1000: 3, 5; remaining cofactor has 19 digits
    Remaining 19-digit cofactor 8230452606740808761 is prime
    [3, 5, 8230452606740808761L]
    
    Smarandache 16
    Factoring 23-digit number
    Wheel factors with B=1000: 2, 2; remaining cofactor has 22 digits
    Rho found 10-digit factor 2507191691 with B=100000, remaining cofactor has 13 digits
    Remaining 13-digit cofactor 1231026625769 is prime
    [2, 2, 2507191691L, 1231026625769L]
    
    Smarandache 17
    Factoring 25-digit number
    Wheel factors with B=1000: 3, 3, 47; remaining cofactor has 22 digits
    Rho found 4-digit factor 4993 with B=100000, remaining cofactor has 18 digits
    Remaining 18-digit cofactor 584538396786764503 is prime
    [3, 3, 47, 4993L, 584538396786764503L]
    
    Smarandache 18
    Factoring 27-digit number
    Wheel factors with B=1000: 2, 3, 3, 97; remaining cofactor has 23 digits
    Rho found 5-digit factor 88241 with B=100000, remaining cofactor has 18 digits
    Remaining 18-digit cofactor 801309546900123763 is prime
    [2, 3, 3, 97, 88241L, 801309546900123763L]
    
    Smarandache 19
    Factoring 29-digit number
    Wheel factors with B=1000: 13, 43, 79, 281; remaining cofactor has 21 digits
    Rho found 4-digit factor 1193 with B=100000, remaining cofactor has 18 digits
    Remaining 18-digit cofactor 833929457045867563 is prime
    [13, 43, 79, 281, 1193L, 833929457045867563L]
    
    Smarandache 20
    Factoring 31-digit number
    Wheel factors with B=1000: 2, 2, 2, 2, 2, 3, 5; remaining cofactor has 28 digits
    Rho found 6-digit factor 323339 with B=100000, remaining cofactor has 22 digits
    Rho found 7-digit factor 3347983 with B=100000, remaining cofactor has 16 digits
    Remaining 16-digit cofactor 2375923237887317 is prime
    [2, 2, 2, 2, 2, 3, 5, 323339L, 3347983L, 2375923237887317L]
    
    Smarandache 21
    Factoring 33-digit number
    Wheel factors with B=1000: 3, 17, 37, 43, 103, 131; remaining cofactor has 24 digits
    Rho found 6-digit factor 140453 with B=100000, remaining cofactor has 18 digits
    Remaining 18-digit cofactor 802851238177109689 is prime
    [3, 17, 37, 43, 103, 131, 140453L, 802851238177109689L]
    
    Smarandache 22
    Factoring 35-digit number
    Wheel factors with B=1000: 2, 7; remaining cofactor has 33 digits
    Rho found 4-digit factor 3169 with B=100000, remaining cofactor has 30 digits
    Rho found 4-digit factor 1427 with B=100000, remaining cofactor has 27 digits
    Rho found 5-digit factor 85829 with B=100000, remaining cofactor has 22 digits
    Remaining 22-digit cofactor 2271991367799686681549 is prime
    [2, 7, 1427L, 3169L, 85829L, 2271991367799686681549L]
    
    Smarandache 23
    Factoring 37-digit number
    Wheel factors with B=1000: 3, 41, 769; remaining cofactor has 32 digits
    Remaining 32-digit cofactor 13052194181136110820214375991629 is prime
    [3, 41, 769, 13052194181136110820214375991629L]
    
    Smarandache 24
    Factoring 39-digit number
    Wheel factors with B=1000: 2, 2, 3, 7; remaining cofactor has 37 digits
    ECM found 19-digit factor 1501601205715706321 in Stage 2 of Curve 12 with B1=2000 and B2=200000, remaining cofactor has 18 digits
    Remaining 18-digit cofactor 978770977394515241 is prime
    [2, 2, 3, 7, 978770977394515241L, 1501601205715706321L]
    
    Smarandache 25
    Factoring 41-digit number
    Wheel factors with B=1000: 5, 5; remaining cofactor has 39 digits
    Rho found 5-digit factor 15461 with B=100000, remaining cofactor has 35 digits
    Rho found 11-digit factor 31309647077 with B=100000, remaining cofactor has 25 digits
    Remaining 25-digit cofactor 1020138683879280489689401 is prime
    [5, 5, 15461L, 31309647077L, 1020138683879280489689401L]
    
    Smarandache 26
    Factoring 43-digit number
    Wheel factors with B=1000: 2, 3, 3, 3, 3; remaining cofactor has 40 digits
    Rho found 5-digit factor 21347 with B=100000, remaining cofactor has 36 digits
    Rho found 7-digit factor 2345807 with B=100000, remaining cofactor has 30 digits
    ECM found 12-digit factor 982658598563 in Stage 2 of Curve 1 with B1=2000 and B2=200000, remaining cofactor has 18 digits
    Remaining 18-digit cofactor 154870313069150249 is prime
    [2, 3, 3, 3, 3, 21347L, 2345807L, 982658598563L, 154870313069150249L]
    
    Smarandache 27
    Factoring 45-digit number
    Wheel factors with B=1000: 3, 3, 3, 19, 19; remaining cofactor has 41 digits
    Rho found 4-digit factor 4547 with B=100000, remaining cofactor has 37 digits
    Rho found 5-digit factor 68891 with B=100000, remaining cofactor has 32 digits
    Remaining 32-digit cofactor 40434918154163992944412000742833 is prime
    [3, 3, 3, 19, 19, 4547L, 68891L, 40434918154163992944412000742833L]
    
    Smarandache 28
    Factoring 47-digit number
    Wheel factors with B=1000: 2, 2, 2, 47, 409; remaining cofactor has 41 digits
    ECM found 15-digit factor 416603295903037 in Stage 2 of Curve 2 with B1=2000 and B2=200000, remaining cofactor has 27 digits
    Remaining 27-digit cofactor 192699737522238137890605091 is prime
    [2, 2, 2, 47, 409, 416603295903037L, 192699737522238137890605091L]
    
    Smarandache 29
    Factoring 49-digit number
    Wheel factors with B=1000: 3, 859; remaining cofactor has 45 digits
    ECM found 20-digit factor 24526282862310130729 in Stage 2 of Curve 55 with B1=11000 and B2=1100000, remaining cofactor has 26 digits
    Remaining 26-digit cofactor 19532994432886141889218213 is prime
    [3, 859, 24526282862310130729L, 19532994432886141889218213L]
    
    Smarandache 30
    Factoring 51-digit number
    Wheel factors with B=1000: 2, 3, 5, 13; remaining cofactor has 48 digits
    Rho found 8-digit factor 49269439 with B=100000, remaining cofactor has 40 digits
    ECM found 18-digit factor 370677592383442753 in Stage 2 of Curve 21 with B1=11000 and B2=1100000, remaining cofactor has 23 digits
    Remaining 23-digit cofactor 17333107067824345178861 is prime
    [2, 3, 5, 13, 49269439L, 370677592383442753L, 17333107067824345178861L]
    
    Smarandache 31
    Factoring 53-digit number
    Wheel factors with B=1000: 29; remaining cofactor has 51 digits
    P-1 found 10-digit factor 2597152967 in Stage 2 with B1=2000 and B2=1000000,remaining cofactor has 42 digits
    Remaining 42-digit cofactor 163915283880121143989433769727058554332117 is prime
    [29, 2597152967L, 163915283880121143989433769727058554332117L]
    
    Smarandache 32
    Factoring 55-digit number
    Wheel factors with B=1000: 2, 2, 3, 7; remaining cofactor has 53 digits
    ECM found 23-digit factor 45068391478912519182079 in Stage 2 of Curve 36 with B1=50000 and B2=5000000, remaining cofactor has 30 digits
    Remaining 30-digit cofactor 326109637274901966196516045637 is prime
    [2, 2, 3, 7, 45068391478912519182079L, 326109637274901966196516045637L]
    
    Smarandache 33
    Factoring 57-digit number
    Wheel factors with B=1000: 3, 23, 269; remaining cofactor has 52 digits
    Rho found 4-digit factor 7547 with B=100000, remaining cofactor has 48 digits
    ECM found 18-digit factor 116620853190351161 in Stage 2 of Curve 3 with B1=11000 and B2=1100000, remaining cofactor has 31 digits
    Remaining 31-digit cofactor 7557237004029029700530634132859 is prime
    [3, 23, 269, 7547L, 116620853190351161L, 7557237004029029700530634132859L]
    
    Smarandache 34
    Factoring 59-digit number
    Wheel factors with B=1000: 2; remaining cofactor has 58 digits
    Remaining 58-digit cofactor 6172839455055606570758085909601061116212631364146515661667 is prime
    [2, 6172839455055606570758085909601061116212631364146515661667L]
    
    Smarandache 35
    Factoring 61-digit number
    Wheel factors with B=1000: 3, 3, 5, 139, 151; remaining cofactor has 55 digits
    Rho found 8-digit factor 64279903 with B=100000, remaining cofactor has 47 digits
    ECM found 10-digit factor 4462548227 in Stage 2 of Curve 2 with B1=2000 and B2=200000, remaining cofactor has 37 digits
    Remaining 37-digit cofactor 4556722495899317991381926119681186927 is prime
    [3, 3, 5, 139, 151, 64279903L, 4462548227L, 4556722495899317991381926119681186927L]
    
    Smarandache 36
    Factoring 63-digit number
    Wheel factors with B=1000: 2, 2, 2, 2, 3, 3, 103, 211; remaining cofactor has 56 digits
    Remaining 56-digit cofactor 39448709943503776711542648338171477043440283875433388943 is prime
    [2, 2, 2, 2, 3, 3, 103, 211, 39448709943503776711542648338171477043440283875433388943L]
    
    Smarandache 37
    Factoring 65-digit number
    Wheel factors with B=1000: 71; remaining cofactor has 63 digits
    Rho found 5-digit factor 12379 with B=100000, remaining cofactor has 59 digits
    Rho found 7-digit factor 4616929 with B=100000, remaining cofactor has 52 digits
    Remaining 52-digit cofactor 3042410911077206144807069396988766146557218727107817 is prime
    [71, 12379L, 4616929L, 3042410911077206144807069396988766146557218727107817L]
    
    Smarandache 38
    Factoring 67-digit number
    Wheel factors with B=1000: 2, 3; remaining cofactor has 66 digits
    ECM found 23-digit factor 86893956354189878775643 in Stage 2 of Curve 67 with B1=50000 and B2=5000000, remaining cofactor has 43 digits
    Remaining 43-digit cofactor 2367958875411463048104007458352976869124861 is prime
    [2, 3, 86893956354189878775643L, 2367958875411463048104007458352976869124861L]
    
    Smarandache 39
    Factoring 69-digit number
    Wheel factors with B=1000: 3, 67, 311; remaining cofactor has 64 digits
    Rho found 4-digit factor 1039 with B=100000, remaining cofactor has 61 digits
    ECM found 25-digit factor 6216157781332031799688469 in Stage 2 of Curve 126 with B1=50000 and B2=5000000, remaining cofactor has 36 digits
    Remaining 36-digit cofactor 305788363093026251381516836994235539 is prime
    [3, 67, 311, 1039L, 6216157781332031799688469L, 305788363093026251381516836994235539L]
    
    Smarandache 40
    Factoring 71-digit number
    Wheel factors with B=1000: 2, 2, 5; remaining cofactor has 69 digits
    Rho found 4-digit factor 3169 with B=100000, remaining cofactor has 66 digits
    Rho found 5-digit factor 60757 with B=100000, remaining cofactor has 61 digits
    Rho found 6-digit factor 579779 with B=100000, remaining cofactor has 55 digits
    P-1 found 10-digit factor 4362289433 in Stage 1 with B1=2000 and B2=1000000,remaining cofactor has 46 digits
    ECM found 20-digit factor 79501124416220680469 in Stage 2 of Curve 48 with B1=50000 and B2=5000000, remaining cofactor has 26 digits
    Remaining 26-digit cofactor 15944694111943672435829023 is prime
    [2, 2, 5, 3169L, 60757L, 579779L, 4362289433L, 79501124416220680469L, 15944694111943672435829023L]
    
    Smarandache 41
    Factoring 73-digit number
    Wheel factors with B=1000: 3, 487; remaining cofactor has 69 digits
    Rho found 8-digit factor 32002651 with B=100000, remaining cofactor has 62 digits
    Rho found 6-digit factor 493127 with B=100000, remaining cofactor has 56 digits
    Remaining 56-digit cofactor 53545135784961981058419604998638516483529257158438201753 is prime
    [3, 487, 493127L, 32002651L, 53545135784961981058419604998638516483529257158438201753L]
    
    Smarandache 42
    Factoring 75-digit number
    Wheel factors with B=1000: 2, 3, 127, 421; remaining cofactor has 69 digits
    P-1 found 11-digit factor 22555732187 in Stage 2 with B1=2000 and B2=1000000,remaining cofactor has 59 digits
    P-1 found 25-digit factor 4562371492227327125110177 in Stage 2 with B1=50000, B2=25000000, and X=2, remaining cofactor has 34 digits
    Remaining 34-digit cofactor 3739644646350764691998599898592229 is prime
    [2, 3, 127, 421, 22555732187L, 4562371492227327125110177L, 3739644646350764691998599898592229L]
    
    Smarandache 43
    Factoring 77-digit number
    Wheel factors with B=1000: 7, 17, 449; remaining cofactor has 72 digits
    Remaining 72-digit cofactor 231058353953907153927797941629430896528705484237484443924582239474910453 is prime
    [7, 17, 449, 231058353953907153927797941629430896528705484237484443924582239474910453L]
    
    Smarandache 44
    Factoring 79-digit number
    Wheel factors with B=1000: 2, 2, 2, 3, 3; remaining cofactor has 77 digits
    Abandoning factorization with 77-digit composite cofactor
    [0, 2, 2, 2, 3, 3, 17146776264043351585439127526669614211701753789295876837964380051922139464227L]
    
    Smarandache 45
    Factoring 81-digit number
    Wheel factors with B=1000: 3, 3, 5, 7, 41, 727; remaining cofactor has 74 digits
    Rho found 4-digit factor 1291 with B=100000, remaining cofactor has 71 digits
    ECM found 13-digit factor 2634831682519 in Stage 2 of Curve 1 with B1=2000 and B2=200000, remaining cofactor has 58 digits
    ECM found 18-digit factor 379655178169650473 in Stage 2 of Curve 16 with B1=11000 and B2=1100000, remaining cofactor has 41 digits
    Remaining 41-digit cofactor 10181639342830457495311038751840866580037 is prime
    [3, 3, 5, 7, 41, 727, 1291L, 2634831682519L, 379655178169650473L, 10181639342830457495311038751840866580037L]
    
    Smarandache 46
    Factoring 83-digit number
    Wheel factors with B=1000: 2, 31, 103; remaining cofactor has 79 digits
    Rho found 9-digit factor 270408101 with B=100000, remaining cofactor has 70 digits
    P-1 found 18-digit factor 374332796208406291 in Stage 2 with B1=2000 and B2=1000000,remaining cofactor has 53 digits
    ECM found 25-digit factor 3890951821355123413169209 in Stage 2 of Curve 58 with B1=11000 and B2=1100000, remaining cofactor has 28 digits
    Remaining 28-digit cofactor 4908543378923330485082351119 is prime
    [2, 31, 103, 270408101L, 374332796208406291L, 3890951821355123413169209L, 4908543378923330485082351119L]
    
    Smarandache 47
    Factoring 85-digit number
    Wheel factors with B=1000: 3; remaining cofactor has 84 digits
    Rho found 4-digit factor 4813 with B=100000, remaining cofactor has 80 digits
    Rho found 6-digit factor 679751 with B=100000, remaining cofactor has 75 digits
    ECM found 22-digit factor 4626659581180187993501 in Stage 2 of Curve 7 with B1=50000 and B2=5000000, remaining cofactor has 53 digits
    Remaining 53-digit cofactor 27186948196033729596487563460186407241534572026740723 is prime
    [3, 4813L, 679751L, 4626659581180187993501L, 27186948196033729596487563460186407241534572026740723L]
    
    Smarandache 48
    Factoring 87-digit number
    Wheel factors with B=1000: 2, 2, 3, 179; remaining cofactor has 83 digits
    Rho found 4-digit factor 1493 with B=100000, remaining cofactor has 80 digits
    Rho found 7-digit factor 1894439 with B=100000, remaining cofactor has 74 digits
    Abandoning factorization with 74-digit composite cofactor
    [0, 2, 2, 3, 179, 1493L, 1894439L, 20320774991535152388175335880426877282982584987974617900489904484536181713L]
    
    Smarandache 49
    Factoring 89-digit number
    Wheel factors with B=1000: 23, 109; remaining cofactor has 85 digits
    Rho found 7-digit factor 3251653 with B=100000, remaining cofactor has 79 digits
    Rho found 10-digit factor 2191196713 with B=100000, remaining cofactor has 69 digits
    ECM found 23-digit factor 53481597817014258108937 in Stage 2 of Curve 294 with B1=50000 and B2=5000000, remaining cofactor has 47 digits
    Remaining 47-digit cofactor 12923219128084505550382930974691083231834648599 is prime
    [23, 109, 3251653L, 2191196713L, 53481597817014258108937L, 12923219128084505550382930974691083231834648599L]
    
    Smarandache 50
    Factoring 91-digit number
    Wheel factors with B=1000: 2, 3, 5, 5, 13, 211; remaining cofactor has 85 digits
    Rho found 5-digit factor 20479 with B=100000, remaining cofactor has 81 digits
    ECM found 18-digit factor 160189818494829241 in Stage 2 of Curve 10 with B1=11000 and B2=1100000, remaining cofactor has 63 digits
    ECM found 20-digit factor 46218039785302111919 in Stage 2 of Curve 66 with B1=11000 and B2=1100000, remaining cofactor has 44 digits
    Remaining 44-digit cofactor 19789860528346995527543912534464764790909391 is prime
    [2, 3, 5, 5, 13, 211, 20479L, 160189818494829241L, 46218039785302111919L, 19789860528346995527543912534464764790909391L]
    
    Smarandache 51
    Factoring 93-digit number
    Wheel factors with B=1000: 3; remaining cofactor has 92 digits
    ECM found 20-digit factor 17708093685609923339 in Stage 2 of Curve 17 with B1=11000 and B2=1100000, remaining cofactor has 73 digits
    Remaining 73-digit cofactor 2323923950500978408934946776574079545611397611995364705071565292612305003 is prime
    [3, 17708093685609923339L, 2323923950500978408934946776574079545611397611995364705071565292612305003L]
    
    Smarandache 52
    Factoring 95-digit number
    Wheel factors with B=1000: 2, 2, 2, 2, 2, 2, 2; remaining cofactor has 92 digits
    ECM found 17-digit factor 43090793230759613 in Stage 2 of Curve 7 with B1=11000 and B2=1100000, remaining cofactor has 76 digits
    Remaining 76-digit cofactor 2238311464092386636761884511894978048448617178182150344531477542781856216843 is prime
    [2, 2, 2, 2, 2, 2, 2, 43090793230759613L, 2238311464092386636761884511894978048448617178182150344531477542781856216843L]
    
    Smarandache 53
    Factoring 97-digit number
    Wheel factors with B=1000: 3, 3, 3, 7, 7, 7; remaining cofactor has 93 digits
    ECM found 18-digit factor 127534541853151177 in Stage 2 of Curve 26 with B1=11000 and B2=1100000, remaining cofactor has 76 digits
    Remaining 76-digit cofactor 1045271879581348729278017817925065799872257805888381045072615907010178634849 is prime
    [3, 3, 3, 7, 7, 7, 127534541853151177L, 1045271879581348729278017817925065799872257805888381045072615907010178634849L]
    
    Smarandache 54
    Factoring 99-digit number
    Wheel factors with B=1000: 2, 3, 3, 3, 3, 3, 3, 79, 389; remaining cofactor has 91 digits
    Rho found 4-digit factor 3167 with B=100000, remaining cofactor has 87 digits
    Rho found 5-digit factor 13309 with B=100000, remaining cofactor has 83 digits
    ECM found 11-digit factor 69526661707 in Stage 2 of Curve 3 with B1=2000 and B2=200000, remaining cofactor has 72 digits
    ECM found 22-digit factor 8786705495566261913717 in Stage 2 of Curve 32 with B1=50000 and B2=5000000, remaining cofactor has 51 digits
    Remaining 51-digit cofactor 107006417566370797549761092803112128112769421435739 is prime
    [2, 3, 3, 3, 3, 3, 3, 79, 389, 3167L, 13309L, 69526661707L, 8786705495566261913717L, 107006417566370797549761092803112128112769421435739L]
  4. fisherro said

    Funny that these days I think of writing a generator function first. I could’ve just included that logic in the loop. I blame all the playing around with ranges (i.e. lazy sequences) that I’ve been doing.

    I reused the isprime function (not shown) that I’d written for an earlier collatz primes exercise.

    #include <sstream>
    #include <string>
    #include <algorithm>
    #include <iterator>
    #include <iostream>
    #include <boost/multiprecision/cpp_int.hpp>
    #include "isprime.hpp"
    
    using Int = boost::multiprecision::cpp_int;
    
    auto triangle = [current = Int(1), oss = std::ostringstream()]() mutable {
        oss << current++;
        return Int(oss.str());
    };
    
    int main()
    {
        while (true) {
            Int candidate = triangle();
            bool prime = isprime(candidate);
            std::cout << candidate << ": " << prime << '\n';
            if (prime) break;
        }
    }
    

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