PrimePredict.ipynb

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     "text": [
      "[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 47, 79, 127, 191, 193, 197, 199, 359, 383, 431, 433, 439, 443, 467, 479, 487, 491, 499, 4099, 4111, 4133, 4157, 4159, 4219, 4223, 4271, 4273, 4337, 4339, 4343, 4919, 4967, 4969, 4973, 18797, 18901, 19093, 19141, 19153, 19441, 19457, 19463, 19469, 19471, 19727, 19729, 19777, 19781, 19783, 20071, 20359, 20551, 20567, 20569, 20593, 20599, 21271, 73111, 73123, 73127, 73133, 73141, 73237, 73309, 73693, 73709, 73961, 73963, 74003, 74147, 74149, 74197, 74203, 74779, 74923, 75043, 76003, 76099, 76103, 76157, 76159, 76831, 77551, 77563, 77569, 77573, 77897, 77899, 77963, 77971, 77983, 78751, 78847, 79279, 79283, 79307, 79309, 79333, 79337]\n",
      "Find next prime: 38.18 %\n",
      "Find true prime: 40.0 %\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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