#! /usr/bin/env python
#	probprim.py v0.0.3, Heiko Stamer <stamer@gaos.org>, http://gaos.org/~stamer
#	probalistic primality tests: RabinMiller, SolovayStrassen, Lehmann
#
# Copyright (C) 1999 <Heiko Stamer>
#
#   This program is free software; you can redistribute it and/or modify
#   it under the terms of the GNU General Public License as published by
#   the Free Software Foundation; either version 2 of the License, or
#   (at your option) any later version.
#
#   This program is distributed in the hope that it will be useful,
#   but WITHOUT ANY WARRANTY; without even the implied warranty of
#   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
#   GNU General Public License for more details.
#
#   You should have received a copy of the GNU General Public License
#   along with this program; if not, write to the Free Software
#   Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.

import whrandom
from time import clock

primes = [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
    47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
    103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
    157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
    211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
    269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
    331, 337, 347, 349, 353, 359, 367, 373, 379, 383,
    389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
    449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
    509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
    587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
    643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
    709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
    773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
    853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
    919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
    991, 997, 1009, 1013, 1019, 1021, 1031, 1033,
    1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
    1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
    1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
    1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277,
    1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307,
    1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
    1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
    1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
    1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
    1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
    1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
    1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
    1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
    1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871,
    1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
    1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
    1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
    2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111,
    2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161,
    2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243,
    2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
    2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
    2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
    2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473,
    2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551,
    2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633,
    2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
    2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729,
    2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791,
    2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851,
    2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917,
    2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
    3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061,
    3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
    3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,
    3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271,
    3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
    3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391,
    3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467,
    3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533,
    3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583,
    3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
    3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709,
    3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779,
    3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
    3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917,
    3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
    4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049,
    4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111,
    4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
    4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243,
    4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
    4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391,
    4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457,
    4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519,
    4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
    4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
    4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729,
    4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799,
    4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
    4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951,
    4957, 4967, 4969, 4973, 4987, 4993, 4999]

def zwei_hoch(x):
    return (1L << x)    

def x_hoch_y_mod_n(x,y,n):
 if (y == 0L):
  return (1L % n)
 s,t,u = 1L,x,y
 while (u != 0L):
  if (u & 1L):
   s = (s * t) % n
  u,t = u >> 1L,(t ** 2L) % n
 return s

def mypow(x,y,n):
 ret = pow(x,y,n)
 if (ret == (n - 1L)):
  return -1L
 else:
  return ret

def ggT(x,y):
 if (x < 0L):
  x = -x
 if (y < 0L):
  y = -y
 if (x + y == 0L):
  return 'ggT ERROR'
 g = y
 while (x > 0L):
  g,x,y = x,y % x,g
 return g

def relativPrim(x,y):
 if (ggT(x,y) == 1L):
  return 1L
 else:
  return 0L

def LegendreSymbol(a,p):
 return mypow(a,((p - 1L) >> 1L),p)
 
def JacobiSymbol(a,b):
 if (b & 1L):
  if (a >= b):
   a = a % b
  if (a == 0L):
   return 0L
  if (a == 1L):
   return 1L
  if (a < 0L):
   if (not(((b - 1L) >> 1L) & 1L)):
    return JacobiSymbol(-a,b)
   else:
    return -JacobiSymbol(-a,b)
  if (not(a & 1L)):
   if (not((((b * b) - 1L) >> 3L) & 1L)):
    return JacobiSymbol(a >> 1L,b)
   else:
    return -JacobiSymbol(a >> 1L,b)
  g = ggT(a,b)
  if (a & 1L):
   if (g == a):
    return 0L
   elif (g != 1L):
    return (JacobiSymbol(g,b) * JacobiSymbol(a / g,b))
   elif (not(((((a - 1L) * b) - 1L) >> 2L) & 1L)):
    return JacobiSymbol(b,a)
   else:
    return -JacobiSymbol(b,a)
  else: 
   return 'JacobiSymbol ERROR'
 else:
  return 'JacobiSymbol ERROR'
  
def randLONG(mi,ma):
 zahl,len = 0L,long(round(whrandom.uniform(mi,ma)))
 while (len > -1L):
  zahl,len = zahl + (long(round(whrandom.uniform(0,1))) * zwei_hoch(len)),len - 1L 
 return zahl

def primLONG(mi,ma):
 zahl,len = 0L,long(round(whrandom.uniform(mi,ma)))
 zahl,len = zwei_hoch(len),len - 1L
 while (len > 0L):
  zahl,len = zahl + (long(round(whrandom.uniform(0,1))) * zwei_hoch(len)),len - 1L 
 return (zahl + 1L)

def div2p(p):
 count = 0L
 while (not(p & 1L)):
  p,count = p >> 1L,count + 1L
 return count

def bitlen(p):
 count = 0L
 while (p > 0L):
  p,count = p - zwei_hoch(count),count + 1L
 return count
 
def RabinMiller(p,t):
 b = div2p(p - 1L)
 while (t > 0L):
  m,a,t = ((p - 1L) >> b),p,t - 1L
  print 'RabinMiller: mit t,b,m =',t,b,m
  while ((a >= p) and (a > 2L)):
   a = randLONG(2L,bitlen(p))
  print 'RabinMiller: mit a =',a
  j,z = 0L,mypow(a,m,p)
  print 'RabinMiller: ',
  if ((z == 1L) or (z == -1L)):
   print '+',
  else:   
   while (1):
    print '-',
    if ((j > 0L) and (z == 1L)):
     return 0L
    j = j + 1L
    if ((j < b) and (z != -1L)):
     z = mypow(z,2L,p)
    elif (z == -1L):
     break
    if ((j == b) and (z != -1L)):
     return 0L
  print     
 return 1L

def SolovayStrassen(p,t):
 while (t > 0L):
  t,a = t - 1L,p
  while ((a >= p) and (a > 2L)):
   a = randLONG(2L,bitlen(p))
  print 'SolovayStrassen: mit t,a,ggT(a,p) =',t,a,ggT(a,p)
  if (ggT(a,p) != 1L):
   return 0L
  j = mypow(a,((p - 1L) >> 1L),p)
  print 'SolovayStrassen: mit j =',j,'vs Jacobi(a,p) =',JacobiSymbol(a,p)
  if (JacobiSymbol(a,p) != j):
   return 0L   
 return 1L

def Lehmann(p,t):
 while (t > 0L):
  t,a = t - 1L,p
  while ((a >= p) and (a > 2L)):
   a = randLONG(2L,bitlen(p))
  print 'Lehmann: mit t,a =',t,a
  j = mypow(a,((p - 1L) >> 1L),p)
  if ((j != -1) and (j != 1)):
   return 0L
 return 1L
 
def PrimSieve(p):
 for x in primes:
  if ((p % x) == 0L):
   print 'PrimeSieve: mit x =',x
   return 0L
 return 1L

# -----------------------------------------------------------------------------
 
minLONG = 153L # 1534L
maxLONG = 153L # 1534L

start_time = clock()
intervall_time = 60.0 # 3600.0	# 1 h
primes_found = 0L
primes_checked = 0L

while ((clock() - start_time) < intervall_time): 
 prim = 0L
 ki = 0L
 k = primLONG(minLONG,maxLONG)
 while ((not prim) and ((clock() - start_time) < intervall_time)):
  print '-----------------------------------------------------------------------'
  
  ############################### +- 2 
  ##################################### 153bit 60.0 sec 17/944
  #####################################                 18/1042
  #####################################                 17/862
  #if (ki & 1L):
  # k = k - (ki << 1L)
  #else:
  # k = k + (ki << 1L)
  #ki = ki + 1L
  
  ############################### + 2 
  ##################################### 153bit 60.0 sec 17/836
  #####################################                 16/1021
  #####################################                 
  k = k + 2L
  
  print 'k =',k
  print 'bitlen(k) =',bitlen(k) 
  test1 = PrimSieve(k)
  if (test1 != 1L):
   primes_checked = primes_checked + 1L
   continue 
  test2 = RabinMiller(k,5L)
  print
  if (test2 != 1L):
   primes_checked = primes_checked + 1L
   continue
  test3 = Lehmann(k,72L)
  print test1, test2, test3
  prim = test1 and test2 and test3
  if (prim):
   primes_found = primes_found + 1L
   primes_checked = primes_checked + 1L
  else:
   primes_checked = primes_checked + 1L 
print 'intervall =',intervall_time,'sec, primes =',primes_found,'/',primes_checked