PrimePredict.ipynb

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     "text": [
      "[2, 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]\n",
      "Find next prime: 99.01 %\n",
      "Find true prime: 99.51 %\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import sympy\n",
    "import math\n",
    "\n",
    "\n",
    "def predict(p,plist):\n",
    "    q=p+2\n",
    "    BOOL=sympy.isprime(q)\n",
    "            \n",
    "    if BOOL:\n",
    "        return q\n",
    "\n",
    "    n_iter=5\n",
    "    n_it=100\n",
    "    w=[]\n",
    "    qmin=2*p\n",
    "    for pp in plist:\n",
    "        w.append(1/(2*pp))\n",
    "    BOOLfirst=True\n",
    "    for r in range(1,n_iter):\n",
    "        for rr in range(n_it):\n",
    "            qclist=random.choices(plist,k=r,weights=w)\n",
    "#        qclist=random.choices(plist,k=r)\n",
    "        \n",
    "            prod=1\n",
    "            for qp in qclist:\n",
    "                prod*=qp\n",
    "            q=p+2*prod\n",
    "            \n",
    "            if BOOLfirst and sympy.isprime(q):\n",
    "                qmin=q\n",
    "                BOOLfirst=False\n",
    "            elif sympy.isprime(q):\n",
    "                if qmin>q:\n",
    "                    qmin=q\n",
    "    if qmin!=2*p:\n",
    "        if sympy.isprime(qmin):\n",
    "            return qmin\n",
    "    else:\n",
    "        return p+2\n",
    "    \n",
    "\n",
    "#plist=[2,3,5,7,11,13,17,19,23,29]\n",
    "#plist=list(sympy.primerange(2,100))\n",
    "plist=[2,3,5]\n",
    "Nmax=200\n",
    "for n in range(Nmax):\n",
    "    q=predict(plist[-1],plist)\n",
    "    plist.append(q)\n",
    "print(plist)\n",
    "\n",
    "pmax=max(plist)\n",
    "p_T=list(sympy.primerange(2,pmax))\n",
    "count=0\n",
    "for m,p in enumerate(plist):\n",
    "    if m!=len(plist)-1:\n",
    "        for n,pp in enumerate(p_T):  \n",
    "            if n!=len(p_T)-1:\n",
    "                if p==pp:\n",
    "                    if plist[m+1]==p_T[n+1]:\n",
    "                        count+=1\n",
    "        \n",
    "print('Find next prime:',round(count/len(plist)*100,2),'%')\n",
    "\n",
    "count=0\n",
    "for p in plist:\n",
    "    if p in p_T:\n",
    "        count+=1\n",
    "        \n",
    "print('Find true prime:',round(count/len(plist)*100,2),'%')"
   ]
  }
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