PrimePredict.ipynb

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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 43, 47, 59, 61, 67, 71, 73, 79, 83, 107, 109, 113, 1433, 2297, 2309, 2311, 2339, 2341, 2917, 4933, 4937, 4943, 4951, 4957, 4973, 5069, 5077, 5081, 5417, 5419, 5431, 5503, 5513, 5897, 5903, 5923, 5927, 5987, 6203, 7643, 7649, 7841, 7853, 7901, 7933, 7937, 7949, 7951, 7963, 9403, 9419, 9421, 9781, 10069, 10453, 10463, 10499, 10501, 10513, 31249, 31253, 31259, 31267, 31271, 31783, 32359, 32363, 32369, 32371, 32377, 32381, 32387, 32443, 32491, 32497, 32689, 32693, 32833, 33073, 33169, 33233, 33401, 33403, 33427, 296083, 297523, 297527, 297623, 297659, 297707, 297709, 297733, 297757, 297761, 297763, 297779, 297811, 297907, 297943]\n",
      "Find next prime: 50.91 %\n",
      "Find true prime: 52.73 %\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import sympy\n",
    "\n",
    "def predict(p,plist):\n",
    "    n_iter=30\n",
    "    n_t=30\n",
    "    qlist=[]\n",
    "    q=p+2\n",
    "    \n",
    "    BOOL=True\n",
    "    for rr in range(1,n_iter):\n",
    "        if not BOOL:\n",
    "            break\n",
    "        rlist=[]\n",
    "        for pp in plist:\n",
    "            rlist.append(pp)\n",
    "        n_test=min(len(rlist),n_t)\n",
    "        rclist=random.sample(rlist,n_test)\n",
    "        \n",
    "        for r in rclist:      \n",
    "            if q%r==0:\n",
    "                BOOL=False\n",
    "                break\n",
    "    if BOOL:\n",
    "        qlist.append(q)\n",
    "                \n",
    "#    return qlist\n",
    "\n",
    "    w=[]\n",
    "    for pp in plist:\n",
    "        w.append(1/pp**3)\n",
    "    for r in range(1,n_iter):\n",
    "        qclist=random.choices(plist,k=r,weights=w)\n",
    "\n",
    "        prod=1\n",
    "        for qp in qclist:\n",
    "            prod*=qp\n",
    "        q=p+2*prod\n",
    "\n",
    "        rlist=[]\n",
    "        for pp in plist:\n",
    "            rlist.append(pp)\n",
    "            \n",
    "        for qp in set(qclist):\n",
    "            rlist.remove(qp)\n",
    "        \n",
    "        BOOL=True\n",
    "        for rr in range(1,n_iter):\n",
    "            if not BOOL:\n",
    "                break\n",
    "            n_test=min(len(rlist),n_t)\n",
    "            rclist=random.sample(rlist,n_test)\n",
    "            for r in rlist:\n",
    "                if q%r==0:\n",
    "                    BOOL=False\n",
    "                    break\n",
    "        if BOOL:\n",
    "            qlist.append(q)\n",
    "\n",
    "    return qlist\n",
    "\n",
    "plist=[2,3,5,7,11,13,17,19,23,29]\n",
    "Nmax=100\n",
    "for n in range(Nmax):\n",
    "    qlist=predict(plist[-1],plist)\n",
    "    qlist.sort()\n",
    "    if qlist==[]:\n",
    "        break\n",
    "    plist.append(qlist[0])\n",
    "    plist.sort()\n",
    "print(plist)\n",
    "\n",
    "pmax=max(plist)\n",
    "count=0\n",
    "for n in range(len(plist)-3):\n",
    "    p_T=list(sympy.primerange(plist[n]+1, min(3*plist[n],pmax)))\n",
    "    if p_T[0]==plist[n+1]:\n",
    "        count+=1\n",
    "        \n",
    "print('Find next prime:',round(count/len(plist)*100,2),'%')\n",
    "\n",
    "p_T=list(sympy.primerange(plist[n]+1, pmax))\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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