Data update

Task/Euclid-Mullin-sequence/FutureBasic/euclid-mullin-sequence.basic

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+//
+// Euclid-Mullin Sequence
+// Using FutureBasic 7.0.35
+//
+// September 2025, R.W.
+//
+
+include "gmp.incl"
+
+_TERMS = 16   // first 16 Euclid–Mullin Sequence
+
+// Return a non-trivial factor of n using Pollard-Rho
+
+void local fn PollardRho( n as mpz_t, out as mpz_t )
+  mpz_t x,y,c,d,absDiff
+  mpz_inits( x, y, c, d, absDiff, 0 )
+  mpz_set_ui( x, 2 ) : mpz_set_ui( y, 2 ) : mpz_set_ui( c, 1 )
+  mpz_set_ui( d, 1 )
+  while fn mpz_cmp_ui( d, 1 ) == 0
+    // x = (x*x + c) mod n
+    mpz_mul( x, x, x ) : mpz_add( x, x, c ) : mpz_mod( x, x, n )
+    // y = f(f(y))
+    mpz_mul( y, y, y ) : mpz_add( y, y, c ) : mpz_mod( y, y, n )
+    mpz_mul( y, y, y ) : mpz_add( y, y, c ) : mpz_mod( y, y, n )
+    // d = gcd(|x-y|, n)
+    mpz_sub( absDiff, x, y ) : mpz_abs( absDiff, absDiff )
+    fn mpz_gcd( d, absDiff, n )
+  wend
+  mpz_set( out, d )
+  mpz_clears( x,y,c,d,absDiff,0 )
+end fn
+
+void local fn EuclidMullin( terms as long )
+  CFStringRef result
+  mpz_t total, tmp, factor
+  mpz_inits( total, tmp, factor, 0 )
+  mpz_set_ui( total, 1 )
+  print @
+  print @"First ";terms;" numbers of Euclid-Mullin sequence"
+  print @
+  long k
+  for k = 1 to _TERMS
+    mpz_add_ui( tmp, total, 1 )        // tmp = total + 1
+    fn PollardRho( tmp, factor )       // factor = some factor of tmp
+    result = fn mpz_cf2( factor )
+    print result
+    mpz_mul( total, total, factor )    // total *= factor
+  next
+
+  mpz_clears( total, tmp, factor, 0 )
+end fn
+
+window 1, @"Euclid-Mullin Sequence"
+
+fn EuclidMullin(_TERMS )
+
+handleEvents