// ------------------------------------------------------------
//  Home primes
//
//  Using FutureBasic 7.0.37
//  November 2025, R.W.
//
//  This code is a lot longer than needed. Simply because I
//  refused to use Pollard Rho (it's very slow and unreliable).
//  So I used pseudo ECM (ECF) for factorization. Much faster.
//
//  Output includes Rosetta Task requiring HP65 to be included
//  it also has the "impossible" HP49 (just click [next]..)
// ------------------------------------------------------------

include "gmp.incl"

CFTimeInterval tim

long gN    // the next starting integer for [Next] batches
// Global mpz_t bigints reused for speed
mpz_t num, den, inv, t1, t2, g

mpz_t pp, tmpN, tmpFactor
mpz_t fm
mpz_t gFactors(31)
int   gFactorCount


// -----------------------------------------------------------
//  Helper: Abbreviate big numeric CFString: head...tail
// -----------------------------------------------------------
local fn AbbrevString( s as CFStringRef, head as int, ¬
  tail as int ) as CFStringRef
  if s == 0 then RETURN @""
  CFStringRef a, b, out
  int nLen
  nLen = len( s )
  if nLen <= head + tail then RETURN s
  a   = left( s, head )
  b   = right( s, tail )
  out = @""
  out = concat( a, @"...", b )
end fn = out

// -----------------------------------------------------------
// Helper: Get mpz_t result and abbreviate if > 43 digits
// -----------------------------------------------------------
local fn Abbrev( ts as mpz_t ) as CFStringRef
  CFStringRef result
  result = fn mpz_cf2( ts )  // FB wrapper mpz_t to CFString
  int nLen
  nLen = len( result )
  if nLen <= 43 then RETURN result
  result = fn AbbrevString( result, 20, 20 )
end fn = result

// -----------------------------------------------------------
// Helper: Convert mpz_t to CFString
// -----------------------------------------------------------
local fn mpz_to_CFString( m as mpz_t ) as CFStringRef
  CFStringRef result = @""
  result = fn mpz_cf2( m )  //FB wrapper mpz_t to CFString base 10
end fn = result
// -----------------------------------------------------------
//  Helper: Is n probably prime?
// -----------------------------------------------------------
local fn IsProbablePrime( n as mpz_t ) as boolean
  int r
  r = fn mpz_probab_prime_p( n, 25 )  // 25 reps should be sufficient
  // r = 0 (composite), 1 (probable prime), 2 (definite prime)
  if r > 0 then RETURN _true
end fn = _false

// ------------------------------------------------------------
//  Small prime test for Int input
//  Uses mpz_probab_prime_p with gmp
// ------------------------------------------------------------
local fn IsPrimeInt( n as long ) as Boolean
  if n < 2 then RETURN _false
  fn mpz_set_si( pp, n )
  int r
  r = fn mpz_probab_prime_p( pp, 15 )
  if r > 0 then RETURN _true
end fn = _false

// -----------------------------------------------------------
//  Helper: Simple 32-bit primality test for Stage 1 ECM
// -----------------------------------------------------------
local fn IsSmallPrime32( p as UInt32 ) as boolean
  if p < 2 then return _false
  if p = 2 then return _true
  if (p AND 1) == 0 then return _false

  UInt32 d
  d = 3
  while d * d <= p
    if (p MOD d) == 0 then return _false
    d = d + 2
  wend

end fn = _true

// Clear global mpz
void local fn clear_MPZ
  mpz_clear( num )
  mpz_clear( den )
  mpz_clear( inv )
  mpz_clear( t1 )
  mpz_clear( t2 )
  mpz_clear( g )
end fn

// Init global mpz
void local fn Init_MPZ
  mpz_init( num )
  mpz_init( den )
  mpz_init( inv )
  mpz_init( t1 )
  mpz_init( t2 )
  mpz_init( g )
end fn

// ---------------------------------------------------------------
//  ECM_PointDouble
//  Point doubling: P = (x,y) → 2P on y^2 = x^3 + a x + b (MOD n)
//  Returns _true if a nontrivial factor found (in 'factor'),
//  else _false.
//  On success, 'factor' holds GCD > 1, < n, and x,y are undefined
//  On normal completion, x,y are updated to 2P.
// ---------------------------------------------------------------

local fn ECM_PointDouble( n as mpz_t, a as mpz_t, ¬
  x as mpz_t, y as mpz_t, factor as mpz_t ) as boolean

  fn Init_MPZ

  mpz_mul( t1, x, x )  // num = 3 * x^2 + a (MOD n)
  mpz_mod( t1, t1, n )       // t1 = x^2
  mpz_mul_ui( num, t1, 3 )   // num = 3*x^2
  mpz_add( num, num, a )
  mpz_mod( num, num, n )

  mpz_mul_ui( den, y, 2 )  // den = 2*y (MOD n)
  mpz_mod( den, den, n )

  if fn mpz_invert( inv, den, n ) == 0  // try to invert den
    // inversion failed -> GCD(den, n) may give a factor?
    // do you feel lucky, punk?
    mpz_GCD( g, den, n )
    if (fn mpz_cmp_ui( g, 1 ) > 0) && (fn mpz_cmp( g, n ) < 0)
      mpz_set( factor, g )
      fn Clear_MPZ
      return _true
    end if
    // GCD == 1 or GCD == n -> useless curve (sigh)
    fn Clear_MPZ
    return _false
  end if

  mpz_mul( t1, num, inv )  // lambda = num * inv (MOD n)
  mpz_mod( t1, t1, n )     // t1 = lambda

  // x3 = lambda^2 - 2 * x (MOD n)
  mpz_mul( t2, t1, t1 )    // lambda^2
  mpz_mod( t2, t2, n )
  mpz_mul_ui( num, x, 2 )  // 2x
  mpz_mod( num, num, n )
  mpz_sub( t2, t2, num )
  mpz_mod( t2, t2, n )     // t2 = x3

  // y3 = lambda * (x - x3) - y (MOD n)
  mpz_sub( num, x, t2 )    // x - x3
  mpz_mod( num, num, n )
  mpz_mul( num, t1, num )  // lambda * (x - x3)
  mpz_mod( num, num, n )
  mpz_sub( num, num, y )   // lambda * (x - x3) - y
  mpz_mod( num, num, n )   // num = y3

  mpz_set( x, t2 )          // update P ← (x3, y3)
  mpz_set( y, num )

  fn Clear_MPZ
end fn = _false

// -----------------------------------------------------------
//  ECM_PointAdd
//  Point addition: P1 = (x1,y1) ← P1 + P2, with P2 = (x2,y2)
//  Curve: y^2 = x^3 + a x + b (MOD n)
//  Returns _true if a factor found (in 'factor'), else _false.
// -----------------------------------------------------------
local fn ECM_PointAdd( n as mpz_t, a as mpz_t, x1 as mpz_t, ¬
  y1 as mpz_t, x2 as mpz_t, y2 as mpz_t, factor as mpz_t ) as boolean

  fn Init_MPZ

  mpz_sub( t1, n, y2 )     // t1 = -y2 MOD n
  mpz_mod( t1, t1, n )
  // If x1 == x2 and y1 == -y2, point is infinity
  // For our purposes, treat this as a useless -> just return _false.
  if (fn mpz_cmp( x1, x2 ) == 0) && (fn mpz_cmp( y1, t1 )== 0)
    fn Clear_MPZ
    return _false
  end if

  mpz_sub( num, y2, y1 )   // num = y2 - y1 (MOD n)
  mpz_mod( num, num, n )

  mpz_sub( den, x2, x1 )   // den = x2 - x1 (MOD n)
  mpz_mod( den, den, n )

  // try to invert den
  if fn mpz_invert( inv, den, n ) == 0
    mpz_GCD( g, den, n )
    if (fn mpz_cmp_ui( g, 1 ) > 0) && (fn mpz_cmp( g, n ) < 0)
      mpz_set( factor, g )
      fn Clear_MPZ
      return _true
    end if
    fn Clear_MPZ
    return _false
  end if

  mpz_mul( t1, num, inv )  // lambda = num * inv (MOD n)
  mpz_mod( t1, t1, n )     // t1 = lambda

  // x3 = lambda^2 - x1 - x2 (MOD n)
  mpz_mul( t2, t1, t1 )    // lambda^2
  mpz_mod( t2, t2, n )
  mpz_sub( t2, t2, x1 )
  mpz_sub( t2, t2, x2 )
  mpz_mod( t2, t2, n )     // t2 = x3

  // y3 = lambda * (x1 - x3) - y1 (MOD n)
  mpz_sub( num, x1, t2 )        // x1 - x3
  mpz_mod( num, num, n )
  mpz_mul( num, t1, num )
  mpz_mod( num, num, n )
  mpz_sub( num, num, y1 )
  mpz_mod( num, num, n )    // num = y3

  mpz_set( x1, t2 )
  mpz_set( y1, num )

  fn Clear_MPZ

end fn = _false

// ------------------------------------------------------------
//  ECM_ScalarMul
//  Scalar multiply P = (x,y) by k:  P ← k * P
//  Uses binary double-and-add. Returns _true if a factor found.
// ------------------------------------------------------------

local fn ECM_ScalarMul( n as mpz_t, a as mpz_t, x as mpz_t, ¬
  y as mpz_t, k as UInt64, factor as mpz_t ) as boolean

  if k <= 1 then return _false

  mpz_t rx, ry, qx, qy
  mpz_init( rx )
  mpz_init( ry )
  mpz_init( qx )
  mpz_init( qy )

  int hasR
  hasR = _false     // R (result) is "not set" yet

  mpz_set( qx, x )  // Q = P (base)
  mpz_set( qy, y )

  // find highest bit of k
  int sbit
  sbit = 63
  while (sbit > 0) && ((k AND (1ULL << sbit)) = 0)
    sbit -- // decrement bit
  wend

  // process bits from MSB down to 0
  while sbit >= 0
    if hasR
      // R = 2R
      if fn ECM_PointDouble( n, a, rx, ry, factor )
        // factor found
        mpz_clear( rx )
        mpz_clear( ry )
        mpz_clear( qx )
        mpz_clear( qy )
        return _true
      end if
    end if

    if (k AND (1ULL << sbit)) != 0
      if hasR = _false
        // first 1 bit: R = Q
        mpz_set( rx, qx )
        mpz_set( ry, qy )
        hasR = _true
      else
        // R = R + Q
        if fn ECM_PointAdd( n, a, rx, ry, qx, qy, factor )
          mpz_clear( rx )
          mpz_clear( ry )
          mpz_clear( qx )
          mpz_clear( qy )
          return _true
        end if
      end if
    end if

    sbit -- // decrement bit
  wend

  if hasR
    mpz_set( x, rx )
    mpz_set( y, ry )
  end if

  mpz_clear( rx )
  mpz_clear( ry )
  mpz_clear( qx )
  mpz_clear( qy )
end fn = _false


// ----------------------------------------------------------------
//  ECM_Stage1Curve
//  Stage-1 ECM on one curve determined by 'sigma'
//  Curve: y^2 = x^3 + a x + b (MOD n) with (x,y) chosen from sigma.
//  B1: first-stage bound, e.g. 10000.
//  Returns _true and sets 'factor' if a factor was
//  found, else _false.
// ----------------------------------------------------------------

local fn ECM_Stage1Curve( n as mpz_t, factor as mpz_t, ¬
  B1 as UInt32, sigma as UInt32 ) as boolean

  mpz_t a, b, x, y, tmp
  mpz_init( a )
  mpz_init( b )
  mpz_init( x )
  mpz_init( y )
  mpz_init( tmp )

  mpz_set_ui( x, sigma )      // x = sigma (MOD n)
  mpz_mod( x, x, n )

  mpz_set_ui( y, sigma + 1 )  // y = sigma + 1 (MOD n)
  mpz_mod( y, y, n )

  mpz_set_ui( a, sigma + 2 )  // a = sigma + 2 (MOD n)
  mpz_mod( a, a, n )

  // b = y^2 - x^3 - a*x (MOD n)
  mpz_mul( b, y, y )          // y^2
  mpz_mod( b, b, n )

  mpz_mul( tmp, x, x )        // x^2
  mpz_mod( tmp, tmp, n )
  mpz_mul( tmp, tmp, x )      // x^3
  mpz_mod( tmp, tmp, n )
  mpz_sub( b, b, tmp )        // y^2 - x^3

  mpz_mul( tmp, a, x )        // a * x
  mpz_mod( tmp, tmp, n )
  mpz_sub( b, b, tmp )        // y^2 - x^3 - a*x
  mpz_mod( b, b, n )

  // Multiply P by prime powers p^e with p <= B1
  UInt32 p, pe
  p = 2

  while p <= B1
    if fn IsSmallPrime32( p )
      // pe = p^e <= B1
      pe = p
      while (pe * p) <= B1
        pe = pe * p
      wend

      if fn ECM_ScalarMul( n, a, x, y, pe, factor )
        // factor found
        mpz_clear( a )
        mpz_clear( b )
        mpz_clear( x )
        mpz_clear( y )
        mpz_clear( tmp )
        return _true
      end if
    end if

    if p == 2 then p = 3 else p = p + 2
  wend

  mpz_clear( a )
  mpz_clear( b )
  mpz_clear( x )
  mpz_clear( y )
  mpz_clear( tmp )
end fn = _false

// -----------------------------------------------------------
//  ECM_FindFactor
//  Try several Stage-1 ECM curves with increasing sigma.
//  Returns _true and sets 'factor' if a factor is found.
// -----------------------------------------------------------

local fn ECM_FindFactor( n as mpz_t, factor as mpz_t ) as boolean
  UInt32 B1, sigma
  int curves
  int i
  B1     = 10000       // bound (bigger = slower)
  curves = 20          // number of different curves to try
  sigma = 2
  i = 0
  while i < curves
    if fn ECM_Stage1Curve( n, factor, B1, sigma )
      return _true
    end if
    sigma ++
    i ++
  wend
end fn = _false

// Safely divide mpz_t

local fn SafeMpzDiv( z as mpz_t, x as mpz_t, y as mpz_t )  as boolean
  if ( fn mpz_sgn( y ) == 0 )  // div by zero?
    mpz_set_ui( z, 0)
    return _false
  end if
  // Call GMP division (truncate toward zero)
  mpz_tdiv_q( z, x, y )
end fn = _true


// -----------------------------------------------------------
//  Recursive factorization using ECM Stage 1
//  Results go into global gFactors() / gFactorCount
//  trustProbPrime = _true  → use IsProbablePrime shortcut
//  trustProbPrime = _false → NEVER trust IsProbablePrime; rely on ECM
// -----------------------------------------------------------
void local fn FactorRec( n as mpz_t, trustProbPrime as boolean )
  // if n == 1 → nothing
  if fn mpz_cmp_ui( n, 1 ) = 0 then RETURN

  // If allowed, trust mpz_probab_prime_p
  if trustProbPrime
    if fn IsProbablePrime( n )
      mpz_set( gFactors( gFactorCount ), n )
      gFactorCount = gFactorCount + 1
      RETURN
    end if
  end if

  mpz_t d, q
  mpz_init( d )
  mpz_init( q )

  Boolean got
  got = fn ECM_FindFactor( n, d )

  if got == _false
    // ECM did not find a nontrivial factor; treat n as final factor
    mpz_set( gFactors( gFactorCount ), n )
    gFactorCount = gFactorCount + 1
    mpz_clear( d )
    mpz_clear( q )
    RETURN
  end if

  if fn SafeMpzDiv( q, n, d )  // q = n / d
    // recurse on d and q with the same mode
    fn FactorRec( d, trustProbPrime )
    fn FactorRec( q, trustProbPrime )
  end if

  mpz_clear( d )
  mpz_clear( q )
end fn

// ------------------------------------------------------------
//  FactorStringUnderscore
//  Factor j into primes and build "p1_p2_p3" as CFStringRef
//  forceFull = _false → use IsProbablePrime shortcut (fast)
//  forceFull = _true  → ignore IsProbablePrime, full ECM
// ------------------------------------------------------------
local fn FactorStringUnderscore( j as mpz_t, forceFull as boolean ) as CFStringRef
  CFStringRef outStr = @""

  // Work copy of j in fm, factor |j|
  fn mpz_set( fm, j )
  fn mpz_abs( fm, fm )

  // If fm < 2, nothing to do
  if fn mpz_cmp_ui( fm, 2 ) < 0 then RETURN outStr

  // Reset factor buffer
  gFactorCount = 0

  // Fill gFactors[0..gFactorCount-1] with prime factors (not sorted)
  // trustProbPrime = NOT forceFull
  Boolean trustProbPrime
  trustProbPrime = _true
  if forceFull then trustProbPrime = _false

  fn FactorRec( fm, trustProbPrime )

  // If FactorRec somehow didn't produce anything, bail out
  if gFactorCount <= 0 then RETURN outStr

  // sort factors in ascending order (same as before)
  int i, jidx
  mpz_t tmp
  mpz_init( tmp )

  i = 0
  while i < gFactorCount - 1
    jidx = i + 1
    while jidx < gFactorCount
      if fn mpz_cmp( gFactors(i), gFactors(jidx) ) > 0
        fn mpz_set( tmp, gFactors(i) )
        fn mpz_set( gFactors(i), gFactors(jidx) )
        fn mpz_set( gFactors(jidx), tmp )
      end if
      jidx++
    wend
    i++
  wend

  mpz_clear( tmp )

  // build "p1_p2_p3_..." string
  outStr = @""
  i = 0
  while i < gFactorCount
    if i > 0
      outStr = concat( outStr, @"_" )
    end if
    outStr = concat( outStr, fn mpz_to_CFString( gFactors(i) ) )
    i++
  wend

end fn = outStr

// ------------------------------------------------------------
//  FactorConcat (ECM-based)
//  Factor j into primes using FactorRec (ECM + primality test),
//  collect factors in ascending order, and concatenate them
// ------------------------------------------------------------
local fn FactorConcat( j as mpz_t ) as CFStringRef
  CFStringRef outStr = @""

  // Work copy of j in fm, factor |j|
  fn mpz_set( fm, j )
  fn mpz_abs( fm, fm )

  // If fm < 2, nothing to do
  if fn mpz_cmp_ui( fm, 2 ) < 0 then RETURN outStr

  // Reset factor buffer
  gFactorCount = 0

  // Fill gFactors[0..gFactorCount-1] with prime factors (not sorted)
  fn FactorRec( fm, _true )   // for chain math, trust probable primes

  // If FactorRec somehow didn't produce anything, bail out
  if gFactorCount <= 0 then RETURN outStr

  // sort factors in ascending order
  int i, jidx
  mpz_t tmp
  mpz_init( tmp )

  i = 0
  while i < gFactorCount - 1
    jidx = i + 1
    while jidx < gFactorCount
      if fn mpz_cmp( gFactors(i), gFactors(jidx) ) > 0
        // swap gFactors(i) and gFactors(jidx)
        fn mpz_set( tmp, gFactors(i) )
        fn mpz_set( gFactors(i), gFactors(jidx) )
        fn mpz_set( gFactors(jidx), tmp )
      end if
      jidx++
    wend
    i++
  wend

  mpz_clear( tmp )

  // build concatenated decimal string of prime factors
  outStr = @""
  i = 0
  while i < gFactorCount
    outStr = concat( outStr, fn mpz_to_CFString( gFactors(i) ) )
    i++
  wend

end fn = outStr


// Max chain length we’re willing to handle
_kMaxChain = 32

// ------------------------------------------------------------
//  Home_Prime_Chain
//  Build Home Prime chain for integer n
//  - Uses FactorConcat (ECM-backed) for factoring
//  - Stops when value is prime OR when no progress is made
// ------------------------------------------------------------
local fn Home_Prime_Chain( n as long ) as CFStringRef
  CFStringRef result = @""
  CFStringRef pad = @"           "
  CFStringRef chain
  CFStringRef nStr, iterStr, tmpCF

  // Guard: n < 2 → empty
  if n < 2 then RETURN result

  // If n is prime: "HPn = n"
  if fn IsPrimeInt( n )
    nStr  = mid( str( n ), 1 )
    chain = concat( @"HP", nStr )
    chain = concat( chain, left( pad, 10 - len( chain ) ), @"= " )
    chain = concat( chain, nStr )
    result = chain
    RETURN result
  end if

  // ----------------------------------------
  // Otherwise, build the chain using GMP
  // h[0..iterCount] hold the successive values
  // ----------------------------------------
  _kMaxSteps = 64
  mpz_t h( _kMaxSteps - 1 )
  int i

  // initialize mpz_t array
  i = 0
  while i < _kMaxSteps
    fn mpz_init( h(i) )
    i++
  wend

  int iterCount
  iterCount = 0

  CFStringRef concatStr
  CFStringRef oneDigit

  // Track previous value to detect "no progress" stalls
  mpz_t prevN
  fn mpz_init( prevN )
  int stalled
  stalled = _false

  // h[0] = initial n
  fn mpz_set_si( h(0), n )
  fn mpz_set_si( tmpN, n )  // current value in the chain

  // iterate until prime, stall, or max steps
  while iterCount < _kMaxSteps
    int isPrime
    isPrime = fn mpz_probab_prime_p( tmpN, 15 )
    if isPrime > 0
      // Probable prime: normal termination
      exit while
    end if

    // Save previous value so we can detect no progress
    fn mpz_set( prevN, tmpN )

    // Not prime: factor tmpN, build concatenation string of prime factors
    concatStr = fn FactorConcat( tmpN )   // decimal string of concatenated factors

    // Build new tmpN from decimal digits of concatStr
    fn mpz_set_ui( tmpN, 0 )

    int L, dpos, digit
    L    = len( concatStr )
    dpos = 1

    while dpos <= L
      // CFString mid() is 0-based: start at dpos-1
      oneDigit = mid( concatStr, dpos - 1, 1 )
      digit    = IntVal( oneDigit )   // CFStringRef → int digit (0–9)
      fn mpz_mul_ui( tmpN, tmpN, 10 )
      fn mpz_add_ui( tmpN, tmpN, digit )
      dpos++
    wend

    // Check for "no progress": new tmpN == prevN ⇒ factoring failed / stalled
    if fn mpz_cmp( tmpN, prevN ) == 0
      stalled = _true
      exit while
    end if

    // Store this term in the chain
    iterCount++
    if iterCount < _kMaxSteps
      fn mpz_set( h(iterCount), tmpN )
    end if
  wend

  // Safety clamp if we bailed by hitting the step cap
  if iterCount >= _kMaxSteps
    iterCount = _kMaxSteps - 1
    stalled   = _true
  end if

  // iterCount is the index of the final value in h[]
  CFStringRef finalStr
  finalStr = fn Abbrev( h(iterCount) )

  // ----------------------------------------------
  // Build the chain in multi-line readable format
  // ----------------------------------------------
  chain = @""

  // First line: HPn(iterCount)
  pad     = @"           "
  nStr    = mid( str( n ), 1 )
  iterStr = mid( str( iterCount ), 1 )

  chain = concat( chain, @"HP" )
  chain = concat( chain, nStr )
  if iterCount > 1
    chain = concat( chain, @" (" )
    chain = concat( chain, iterStr )
    chain = concat( chain, @")" )
  end if
  chain = concat( chain, left( pad, 10 - len( chain ) ), @"= " )

  // ----------------------------------------------------
  // Print each step on its own line, as factor strings:
  //  stepIndex = 1 → factors of h(0) (original n)
  //  stepIndex = 2 → factors of h(1), etc.
  //  remaining = iterCount - stepIndex
  // ----------------------------------------------------
  int stepIndex
  stepIndex = 1
  while stepIndex <= iterCount - 1
    int remaining
    remaining = iterCount - stepIndex

    // Factor h(stepIndex-1) and show "p1_p2_p3"
    // For intermediate steps we can use the fast mode (trust probable primes).
    tmpCF = fn FactorStringUnderscore( h(stepIndex - 1), _false )
    iterStr = mid( str( remaining ), 1 )

    if stepIndex == 1
      pad = @""
    else
      pad = @"            "
    end if

    chain = concat( chain, pad )
    tmpCF = fn AbbrevString( tmpCF, 20, 20 )
    chain = concat( chain, tmpCF )
    chain = concat( chain, @" (" )
    chain = concat( chain, iterStr )
    chain = concat( chain, @")" )
    chain = concat( chain, @"\n" )

    stepIndex++
  wend

  // Final line: just show the final value (probable prime)
  if stepIndex > 1
    chain = concat( chain, @"            " )
  end if

  //CFStringRef finalStr
  finalStr = fn Abbrev( h(iterCount) )
  chain = concat( chain, finalStr )
  if stalled
    chain = concat( chain, @"  (stalled – factoring limit)" )
  end if

  result = chain

  // clear h[] and prevN
  i = 0
  while i < _kMaxSteps
    fn mpz_clear( h(i) )
    i++
  wend
  fn mpz_clear( prevN )

end fn = result

// ------------------------------------------------------------
//  More_HP
//  show the next 20 Home Primes
// ------------------------------------------------------------
void local fn More_HP
  CFStringRef pline
  long n
  int count

  tim = fn CACurrentMediaTime

  count = 0
  n = gN
  while count < 20
    pline = fn Home_Prime_Chain( n )
    print @pline
    n++
    count++
  wend

  gN = n
  if gN > 160 then button 2, NO
  printf @"\nElapsed time: %.3f secs\n", ( fn CACurrentMediaTime - tim )
end fn

// ------------------------------------------------------------
//  Main — compute 2 to 20 Home primes
// ------------------------------------------------------------
local fn Main
  CFStringRef pline
  long k
  // init globals
  fn mpz_init( pp )
  fn mpz_init( tmpN )
  fn mpz_init( tmpFactor )

  int i
  i = 0
  while i <= 30
    mpz_init( gFactors(i) )
    i++
  wend

  print @"Home Prime for integer 2 through 20:\n"

  tim = fn CACurrentMediaTime

  k = 2
  while k <= 20
    pline = fn Home_Prime_Chain( k )
    print @pline
    k++
  wend

  printf @"\nElapsed time: %.3f secs\n", ( fn CACurrentMediaTime - tim )
  print @"Click [Next] for the next 20 Home primes.\n"

  // Prepare next batch start
  gN = 21
end fn

// ------------------------------------------------------------
//  Dialog handler
// ------------------------------------------------------------
void local fn DoDialog( ev as long, tag as long, wnd as long, obj as CFTypeRef )
  select ( ev )
    case _btnClick
      select ( tag )
        case 2
          fn More_HP
      end select

    case _windowShouldClose
      // clear any uncleared mpz
      fn mpz_clear( pp )
      fn mpz_clear( tmpN )
      fn mpz_clear( tmpFactor )
      end
  end select
end fn

on dialog fn DoDialog

// ------------------------------------------------------------
//  Main
// ------------------------------------------------------------
window 1, @"Home primes", (0,0,800,600)
button 2, YES,, @"Next", (680,20,100,20),,, 1

// init globals
fn mpz_init( pp )
fn mpz_init( tmpN )
fn mpz_init( tmpFactor )

fn Main

HandleEvents