StochasticFactorizatoin.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "09590429",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count= 470\n",
      "47.0 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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O+v4d4PPA/cCfMHh3R1N9A+9n8BrB1xmcab/xbHoE5rvn6SHgFrpP9k+6+dF/SWrEWrvkIklagYEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGvG/w7dxMkwMUsEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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lx2iYHz6WDyNDCKBaH4PAqu2Q6LSaUHPOq5L/1wD4N4BJgjLPcs7LOeflZWVl/vaS6Pbs2t+Cn7yxAu2xOLbVidfuUyHCvKUfFR2pvfrf8sLngVp72UY16mPZ9v32lSm4Pqxs6j9/vAkz1+xJV6VTz7Dmj/YbW6FmjPVijPXRPgO4GID1qpgEEQC3vVSB1yt2YaNgYVInRHWDiX5hVZtMRMzJ/MOO7Nk2Y9Ue651J7FwIsiRTUreTT1+l1XcVlq9GxaIeAmA+Y2wFgCUAZnDOZwbbLYIAnp67Gev3NABASqBLCr2NfzPG8FoyTExFIGVi+8WO/fjbp1st3QKqIhLWwS7V/ovO/81luwx/W11qQ3ieYr+y+WALIlOfG2zjqDnnWwGclIW+EESKWGccj87cgL98vBlrHrgkZdF5taDWVB3E/uTkFTcuEL0oXfP0QgBAYVT/Kp5GNR91WFHtv6ic+eFjp3cc5KOWQeF5RGhYtmM/ahsTuZK1FVXMWvrJRuuB6idnb8LrFTulbdQ1pfMKqwwmqqAfKNP3N891Wrn/Ks87q8HEuGHwMpjwPC+ERKdpCjkRHq59eiGG9S3BwnsvQGtHQkTNro4HZ6yzPP6JjzYCAL5WPsKyTJMuMkO2vJaG2sKo+vLBKUdYhd/LOXt9sPk1mGhZS0hMarKoiZzy4oJt+O37afGtSr4ytyZFtKQw6mt7ja3pJPttHXKLetmO/VhpSjkquqGtFmgNq7CqorxaucOHmVUbyhOEHLbtBLPwh0OmyaImcsz97yQyxt1zyTGG7YcUhJpz7niwR5+BrjUmt6ivTfqg7TC6Prjwsxk3+pIN487N4J5KFI1V1/V5UnIaamdxDiExqMmiJsJBR6fxRtEs6uIC65+om3Bo/Y3nNhG/rM64C6FTJdsWuq+DoRaC58b1YYyj7h6QUBNZoakthqWSiRGxuNENoYmozKJ2E7Whz5hnZVG3tMdcDzSqJtvPB1Qvr9Vp6s/fbjDR7ZUK+hqHZQo5uT6IrHDn1GX4dGMtVt1/MfqUFGbs74gZb7hDSha1C6HW3XixTvHx4+/7AOVH9FeuU38rG6MY8htlH7XFmcY5oEUuWvuoxZ9V8esaW9UTDpkmi5oIkHXVDalloNYkk+K3WgzgtZsW5dNcIUUSoY65sKj1giGzyCssrH+RmOitLqPw5J9U60XXq0U9e93e1GdLH3Vc81E7WDjAJW6+jpAY1CTUhP+0tMewtqoBl/5pHv532hfgnKfWJ7Sygs2uDxWR0wutGzeIuS+uc4Dooz50m61OYdWug/hUEg8eFlTfWKxK3fGPpdhen8jLYjXo62qcQfe54VAH7n59ufNKTIT9mUquD8J3LvvTPFTWt6T+jvNEMiTAWgzNrg+tmCyqQ1/XpIdmKfVN34rZIl+8rR5nHDlIqR49Tl0fVz4133Eb2cKQ2tSH/KXaCuhWX6PeR+1GLJ/5ZEtqVXk/0M+o5JyHJgUtWdSEL3DO8dCMtdhc02QQaQD46jML0ZSMX7YU6rjZJeLMoq5vbpeUFFdr7osmKk5hlq4PV9WFBuX+S8pp7gzLXB9q1RiwirLxgvYGZ04AFRbXB1nUhGfmbqjBv7/YjbeWV+GDNXsz9i/bcSD1ub0zjreW78bkMQMN69h1dJpdH/btuhlMNOTiMN3lrQozFe1QjaPOB7zk+jBjO+GFu/TpOzjEqehynkdJmQhCxuVPzsOaqobU33Y37cFDHbjrteUYO7g3Zt19Tmq72fWh/SW7TdwMJurFwHx8m8uQPKOF53ymXVjxo/tp14FKrg/nBD6FPCSQUBOOicc5bn5hCYb17WEQacBenDSrdY8pu5re9bFzX4uaRR3n6IxzfLDGPh+y8Hju3KIWdcvgo9ZpfT4mtddfEtXBVVmplOvDZsILh3U+ahl+uT5EcFB4HpHH/LNiJ+ZtqsM/bTLVibCKXe7QWbM3/G2RksjF4hyvLNqOO6cuc9wPIFOIlFwfAjWxmhSR9xa1Yv9VBN1uCnmyRbUGoR8TCPYih8TzQUJNOGfDHverrJjD8DT+Z9oXqc8HWzqURKIzzrHdNHBph8FHbWpj5z5ndWnoBzL1opXvQu2nj93K15tyUXN318u/wUTRNk5CTeQP9U1tOOvRj1OrrChHWAhoj4nvrJpkHmogkeRH5f7rjHMlMVHN0PbSZ9sVWpXjNb9ymMhG7/UDum6iPoLuI4XnEXnB7z/cgHMem4ud+w7hb59uBQC0tMVsjrJGi+6QvbLGOU/tl1k06kKt+xz07DeLdvMF/fXxsgiwKp1eB199ushWtYTFoqbBRELIuuoGLN5ajz9/vDm1rbAggjeX7sLs9TWu6zWH4YmI616DGYAnPtxgUY4LxcSc/nRqco3ExD5n/c2o226/4aHgLy8urPS5xtxjdH2oXTHjBCP/+6QRpucsCTUh5NI/zcvYVhSN4Ef/WiE9zu5m07LSyUrF48a8D0/qHhZ6YnEuvFG1mz4SYahpbMUv/7PasM+KoX1LrHcqHJ/Y33XiqP0gLcTiaxGa8LyQf1fk+iCU0S/i6hY1i1otVKszzoU32EufVWLMz95DfVObo9d3lTbthKErxVH7idWl8Hq9grzGYfr+SKgJAMDLn1XijaW7pGUKo/Y/F7uZXCqTSgyuD5tcHyKr9fWKxHlUHWh1NBikYp1ZBK2k9xuqCNGdrkj2FyfQte3ielk9h2eurnbZIyNhEWtyfRAAgPveWgMAuO6U4ZZlVITa7hVSdfZfk8KAZael6yO90clgkIrxbefOIItajN3iAhxc+bmmspjwd13G1uvhCD71qipkURPKyHJDq6Li+gCAX729xrZMnMujPpZu34dd+42x0dJ1DFVcH7Y+an1b9vXZt5ddoci2LBlncvqHX5ctLA9bZYuaMRYFUAFgN+f8iuC6RIQVP3zUqcFEH26AWFzsy9a2aQvn6pFbxPadslvI1e+luBKJgTxXEwLkg4lOJrxYLSbsBavfUViE2omJdBeAdUF1hMgOm/Y2uhYQFdeHHU7XIpRplJbrw4zsdVVm5frh+jDEBdtXZwsHsHBLHfZ7mGQUBqwum/6az9vsfDGFLIR6hwKlO48xNhzA5QD+Hmx3iCBZtmM/LvrDp3hu/jZXxyv5qG32a2shqvr+ZNZkzGIwUaalsoeUygPMroibVbVltMfi+K+/LcbNLyzxXlkISfuogf/7ZKvr49XKSvZZ/B7D8hxQNZH+COAnACzNIcbYHYyxCsZYRW1t+JcZ6o5U1iWWRTJnvFNFdUXmiKTY1MU7rHc6pNPC9SFDZoGpVGX7qm0Qau+3uZZV0Et+lTBgdSW8XqGghTQs8dW2Qs0YuwJADed8qawc5/xZznk557y8rKzMtw4S/qHlX1YVXDOq07VVkq378fu3Cs+TTqaRNNza0WmbQS/rro9s60TWw/PSPmpVjFEfxn3vr6rGI++vd9wPSx+145qCQWUw8UwAX2aMXQagBEApY+wVzvmNwXaN8AvOOUbf+x4G9ykGALh1NZuti6JoJGP1cMDfHL6NrdZhep0WUR/SPCISk7q1I45jfjlT2p+d+w5J9/senscN/+Utdj5qt4OC5u/aj7A8YwP+VucW21uWc34v53w453wUgK8D+JhEOr/QbgYtQ1004k6pzRonurkYc2+xi1i8zXrh0rhVHLWkvuBflfVt+RD1kQWlONCSu4FK7TekGrYJBJPrQ1QNxVETgfHW8t14f5VxVpY5B7Rbi9oszJYDeVkKJ4tZTCGXLraaxfvOnzhq73XIeGdFFSY88BG+2LE/kPqveXoBOLf4npC2iJ1GA6WOD4mQBo2jW5ZzPpdiqMNJXVMbNu1txF2vLc94/TNPey7wyaK2ukVkg4l+8v6qaszdkDlw7dZH7Td+DETZxW17ZeGWegDA2urEALPfwtfRmXjrsapV+226Wf8ScO/bVq07JGOJNIW8q1D+4CzLCSlmi9rONfHpRnHUjll4rH7EKq4PP37/VulW7XJdZws/WtL62yXmvAhw4/rQE/QMxJDoNLk+uhIdFusRmieFFEQZOjrjqG9qE5b/xvPimF1VkQuzqGR1goSPro9s+tb9r9s6jFL7Ppy4PvRRRUGGz3GEx6Imoe4GmF8rOzrjOOrn7+OUB2fh4KEO5XpURI6DK4XnBak80sFEizsvCHeNH9Z7Nt8ADrZ04PNK/33VKt+Ha4tasdzuA/JoHesJL+FQahLqboBstW2VLHUa+WJRy/pp9bDxM1JFww+NzdYbAGPA3+Y5nxmoQiIeWXwiadeHuxNV/U3ebPGWKCMsk10AEuq8Y/6mOtz64ue2EzP0mIU6qjMfF22px/OKU8ofnSleEktPGJIIye4vqxs7EKH2oQ5Z3LffRAIaBZalMNVOz61FrXp57N4crdOwOuxQQNBgYh7x7soqfP/VLwAkXuWOLOutdFyGUOtEyW5pLTcEdcP7gdWNF8TDxa/seYkPnquyJRdfm6s4asnMRD/hoMFEwgWaSAPAoXZ1i9pJ6JNXcWEs964PNwRhUfthDGfTRx3ENQDkU7HnbaoD4D6OOnApDYlJTUKdJ5gFtMVGqDfXNOLapxegqS2GTrv1o3Q84yKDmR7lXB8B3mBu7q1grMn8GUzk3OgSyzbufdQ+d0RHmHJ9kFCHGL04m5ewam6XDwI+OnMDlu04gPmb6jIsapmQLtpa76KnRnLt+XDzVhCEu+Y7r3jPOxG0UOt/CkGNLahMHPEr10dXhYQ6pFQdOITR976H/3yxGwDQ0GocDHHk+nBprbgnO9nzLOt2cUxQr/1eyWbcd2CuD4VvxO0MQ99yfVikIgjLc4CEOqTs3JdY62/q4u0AMrPINXsIq5NZL37cqyrGaSzOHZ2DH8jOLddvAVak0oBm4SU8qGsgC8/TCKtFHRaLnaI+Qkppj0IAQH1yCSazqGkrpZz3+Fw0tspDj8yuD9HyVX7BoX7D7zQtPOtbH6wiOyDLTxJOpdaGF4L6yhp0YWvBWdT+uj70ayb6dVnEBnVYpruQUIcW7Z7ZlxTqDB91W0KotyVXbZFhFuYghRow3kgy3I/0y7G6vRhjloqRzegKJ6QT6wfTv3dXpjMt5nIw0e1PMuivLSw/C3J9hIDqg4cw6p4Z+FfFztQ27QeiWdJmUTtkM5ioH2w0+6gDtai5ukXtdpKDHVanJ+tWSO7HDLTvKhu+6uDC84KzTP16gIlqCYtIAyTUoeD0334MAPj5v1cDABpbO/BxMjOc9mMxC3WzzWDigs3p6I0Mi1ryCxSlDXWKUq4PAO2xYO6E2kZxsqmQejekXP30gqy1FdzMxOBwUrcb4Q2LVpPrI0Ror7mTHpqd8kFr28yuD7s4aj1mYZ6+bLeXbkppausAUKhUVrSMV5AwqZfaP44Y2BPb6/3xv2fTqgt0MNHHEzFGffhkUYuDPkIzmEgWdY6YuXoPXte5OoD0j+6QLo9HKg1kpzPXh56nPt7kspfOae2Io84ifaqZ774iXS/ZfyRC5Of9WOR2CZ0cE9iAasCTUroDZFHngLkbavCdpEh9rXxEarvMD+nU9WE4Nutx1Go4eSvwgyA9H9EIS7mYwhpBYkdgFrXP0RP6bgbqVpHk0c42+fnoz1PicY4DLe1YsLlOWkZE5mCiqshxHDVYLXlTVydIAdXXHCadvnj8EDxz4ylKZQN9wAQkeP4NJoZEkS0goc4iv3xrNSY88JHlYBdgPdDXHjMKsxPfXFhDz846alBW2wtSh4xTscOj1F85ZTjOO6bMtlwi/j2Yfs8wLbbsJ4Hm+oBcwLPpvyahzhLTluzA1MU7AAC1Eh+ulaiafdTq4stC8/pmJuh4bjPS8DyvWQN1tYdHphN9UY1rDyqO+uf/Xh2YxeqbRW1RTVjuHRLqLDFz9R6lclaJ7syuD3WN46EZuTaTdaEO1KROf8zVxJExZb08HR+iFwEphjUTA2zHLnteViNystdU98YqEkLL5aFx64ufC8uZBwSdiG+W9VCZOOcY2Ksoa+05WXbMKXqNi0QYHr7mhMDasqK4IJqxjTGmLMBBPmCCEjW3yZwy6vGh/iAhoQ6Q216qwLsrqwAAa6oahGW0SS4an1mkGTXnlI5z1ZSkzBcftVdrTUQsztGruABXTxjme93ZRi8CBRGGCSP6Zb0PxQXi21lFfp24SNzgp+Bl6w2R28SrZFPDbYWaMVbCGFvCGFvBGFvDGPt1NjrWFZi1bq9hVRa3NLR2YF+zMfFSnHN8/dlFCkf7E2J0vS6M0C+0CBevLokwZL7Ti1yUMRREs9+pksLM25lB/fqGPfIhUMJiOlugEkfdBuB8znkTY6wQwHzG2PuccxWV6Ha0tMewaGs9zj9miGUZp7PWTrz/w4xtqu4Mzv2J+ggiIqCT+xNhW1wQNUwScoPXXugvTySSm1hqkesDULOoVTLcecHPqrMmqVx+TRKWfXa+Z1uLmidoSv5ZmPwX7sdPjuCcY/x9H+DWFyuwuabJsF3Prv2HfGlLhZc+q8RHa/d6bs+sOwU+mLGxzoS177UmkSUpYuptp3lsyRr9ORREIjkZUBQ16eR50Z1v6rCfu9IvnDEWZYwtB1AD4CPO+WJBmTsYYxWMsYraWu+JffIR/bpv+vzRQUQ3qFrJi7buc7S4rRVmC9GPBD6NrTFUH2xVUuqvlQ+33FegOGW7R5HY4vSbXftbfHmQ+UUYojn89Ctny0uRd7k+OOednPMJAIYDmMQYO15Q5lnOeTnnvLyszD7AvisRj3M8/sEG7DnYmtqm/3qDSD7kYL1aXzBbiFYDV07YfeAQOuMcDAyz7j4HE0f2c1WPam6NHoXBCbXeD1xZ3xJYJjrVPqS3OfBRh0SUwoTU9ZG9bjjL9cE5P8AYmwvgEgCrbYp3GxZtq8dTczYbIjb0P/qOANJ5iizqgb2K0BaLBxKGZtad0pLCjOXB3MIYMHZwb5T1LnZ1vOrAXU+ZRe3xKzL3IBcWdQgMZ0v89VH7fz8Js+eF6LmlEvVRxhjrl/zcA8CFANYH3K+8QnNt6JfE0nsb3kmG6PmJ6Ef0yyvG46FrMl52fMFslfUp8S+fl4rAyAbnVETxqgnD5K4Pjypn7l4uBhNFTToJuQt0MDFEoueEfJrwMhTAHMbYSgCfI+GjfjfYboUfzjneX1WN9lg8dTPoZw/qLepf/Mf/lw+RRc2Y/wIxpDRh5ZpdH6Ulajmn/cJ8WicO74vDSksAAIUKro/LThgqdX2o1CHvn7GDufFRu2/zQHM7fvDP5f51JUD8FMgZK6txwv0fCN2T3KfQVj9QifpYyTmfyDk/kXN+POf8gWx0LOx8uqkO3526DE98tDHlFtAn9w96NqBIqCOM+SrUd5w9JiWG0SAtahddPmpwH5w0oi8AdZEtkQi11yiNDIs6LIOJyW68ers84mXRNpXJU14IieKZePi9dWhsjRnGl/TIJ7xQUqZQ09QWQ31ySvjGvY2pm0G/BmDQGetE1UcYg5856yOMpX6KZiHSVkn3A5XXc9mAWKGCj5oh82FjqMOjsJ451pgJMCc+akmTfW2+r3xa7KBGkn3SKcXJ0M5Wizj8vLGoCSMPzViL43/1ASqTk1a0tQ0Bs0Ud7Dcstqj9dX3otcZscfYoiirHL4sY3Cc9cKjS5RLTZA7G0gKvEp5nznnxyreMFmbUw0zC88aV4fdfPclYX0gGE1nqf3l/inyI4pHh5+3g5+r12iQh81J3gH2fw+ajJpJwzvG3edsAAE/OTi9vpd0EbQYfdbB9EblWmM+ujwhLp0g11xtlDOOG9HFdt97idNtl7dVTxRo0T6WeYsqFLbO27Rg9qHeGWyUnQu2hySKLWY1dCdE9qYWZWlrUQXbIASTUiszfVIfR974n3KfdIPonfdApPHfsy5yGHmH+CkQkwlJiaPa5Rpj1lGUVjK4M531mSN94fuTV8Nun7EX43SKymrXrbNcdP+LiZYRF8Mxob4WtIosaCI3vg4RagZ37WnDjcxmTMaXEsj0jBcnBRD+Fmok/AwkB8PJQcHqsaOBG21IQUXF9yPd78SmL6s7NhBf3xwb9YAmJ3iXQ9SXl+iCLOv9ZtmO/dH+HILSnIwcLyibC8/yrT+b6iHjMEBeVuD6+dFxmQivzjc5YepvSYKJNkahJ7HORptQrMreX3fmHdbm2oNHeJER+b1rcNs+I2Yiu6Eu2OyYIiguivlpGejHNFGo1q3j6nWcIt+sPNdeinhkwUVA114eMPAp6sMbDVx90OGmYUqjq+1KcHFuw8lFL66HBxHBh58YQjRiLjnnw6uNxsst8FioUF0Z8feVmDDhiYE8AmXHTjKm9LhdauCVkFrXKDcB0CyKohNbZRT2YLWoRf/3vky3qDgcii1p7mNmd/5vLdgXSpzCi/31pvx3zCkpaubA8YPybtdCFscs+V1nfnHmM4Is/cXhf7D5wCMt2HPCrawaKCyJo7fDPNx5hDI9edxKumTgcR5b1ztin8lCw0nLjYrDGQqrJgbRSSv5uhz5qUb8vPWGoUr9yRVgeGCLC4kJwijwpE014ySkNrR3YtT8dVWEXwfHozA0Z20THRCMs0EEb2cw7N0QZQ+/iAlw0fohwMNHpANy3zx6jOx7Cz4B4AMcs3noftYqv3K5ELqI0/EZ2Crk+vVzrtP70xX1xsjX7kFCb2HOwFSfe/yGm/G4OHnk/kXvKzcBgh8D1EY2wQJeNKi6IIOZjSlWjmNr7qEcO6CmtY8KIfrjkuMNs23VqUatEfdjx3fOOdH1srkVQIxeJoPIFy19U8pJZ2WLyFV689MgZJNQ6WtpjmPzb2am/n/lkC4DMhWVVEFrUjHleH1BGcUHUl0UCNIyDicZ9EYFFbfUqqEVxWAm/ymAizzg+Legqrg/ZdZ919zk4b9xgVD5yuW09Kjxzo9iXHTSiMwyLRRimXNeiroiiXkLUZRJqPWf9bo5wuxvxE1nhCYvaXlTGDu7tKulRSWHE14k2+r6Koj7MLYmeZwzM8IMXpuI0bbQKFTP3IeX6UBpMtGbs4N6Svc45KUehfbKHEdna8jefuMV9E5bBRBLqJC3tMdQ3twv3uQm1E7kgVF0f15ePcPUaW1wQFcZ0uyVismANMKaUc4EZBN3ailbBNNyXEnS1XB9e2nJ6bG5kMV89H9lOCCWbPJVRLiQrvJBQA1hb1YDx931gud+NRS06xmukhB3FBeoW9Y2TR9qWiRhC6MwyKQ5LNGN2V4gtauPfVqttWFnUKhNeskmuBFPWbK5FXDqhJod9m75sNwBrN0c47GkSajS2duDh99ZJy7gZoPu8cl/GtoKoMYPbH6+fIDw2Ysr0psLgPsWIRBgmjxloyExnxXWnjLAtY3R9GPcxBrTFjJMErPyQ+s23nzUGPQqjOOPIgem6THeq0F8IbrihE5a6Ax91gGqQ8RDLkfCEeTBROsyTZTXUfl41jekc1FY+aplvPZt+924v1N99ZRnmb66TlnHj9527IXMl9qgpu91F4zOnSgPuEis9lkyz2b9XEZb8/ELb8iotGHN9mC1qRddHIn1Sqs2JI/tj3W8uwUDJ+ohWPmPzZXHko/ZJw/77NPs3kVC5PlI/3dyKeDamqDv9jvUuTav+BT1jU5VuL9Srdh+0LeNXJEXE5KO2WmxVpDtTxg7CDZNGYOkvLsTVE4Zl7A/CzycbTAQyp86LrpI+3lk14uWMIwdh1t3nGOvm5kky6fYG9LJ/g/BLph665gS8+z9T5G3lyvURcLu3TRnt+thsGJ9S14/us6grVpFGsgcM+ahDhl+xyQWmqA8r4RJtf+W20/Dba0/EwN7F6BD8qoodJvFX+ZEZ+5q5f+LI/sY6BZUyi892RrDIqs7oQ7K9HkURvPDNU+UVBoi5W7lzQUiiPnzo0uk6d5VTcp30ya51FbddLun2Qq3yA/bTolaxKqMR+ctza3tmAhlzPuH7rhgvbUPFvyZLysQY8LPLjsVHPzzbth4rSzu9374vHJkPDu3mjySWe/EVL/HuOZPpgBv2Ur/sFvIrBE65FsFvX2hRc27jo1Zt0DvdXqhV8CsTXsJHbdwmStKkL/PDC4/G298/07D/kCDT14BeRYa/b50yGgNN2/SonJF+eaaMwcTk/qN0q7yIbjj9xBQvNzrnmccbhDpEqHbnpVsn+duuYBvXjQ94rt/DdQ5LPLIV5KMOOSo/PRWLupeFv1mPaMLL9DvPxJdPMvqc9auJ3zh5JE4c3s+wvyVpUY8p6wUgMcA1tG+PjPZkoYAq1kBUFp4nqFpcp3iBXP11ULVMjG6UdL0RZnwDEQ0u+nm/2emVqqD5vQBu4Ba1h2OlFrVPX47qGofiXDKCbci9y0aj2wu1CiqrtWirPMtmFKpOeIkwhqm3n4bbpozOsJSBdO5cbcFXs684XY+sFfsfYIHB9WHcJxIjOxeHV8xtphc1APr3TF8nlfBET/2wkSzVc87me4AfqQu8vLmEaQq5E6Q2WphcH4yxEYyxOYyxdYyxNYyxu7LRsSCoa8pcZt78A/7+eWMNf09ftgtvLa/CiAE9MKTUWgD6lCSEWvZ7VM31wRhwzGGl+MUV44XlNdeHNoBoVaMsI5zKfaOf8afSb6vBxFTUhydp4pm5PnR9O2lEP1xfPkK5r74icAu5Oc57N4I9b08+aoniZVvCZZZ1ZrlwPGBULOoYgB9xzo8FMBnA9xhj8pGqEDJ/Ux3KH5yFOetrpOV6mFwYd7++AgBQ1rsYp4+xHvXunbSkZTHXEYtcH+ZNdjmlD7UbLWrLnM8yoZa2kECWkF9sIVnlS9A6lN7mxjrLOCblo078ec64skQzPuiVlypUz81vYZW5o7y0pC0A68WiDouvV4+KlS97mQ5VPmrOeTXnfFnycyOAdQAOD7JTczbUYPHWeuxtaLUvrMjynfsBAEu3709tu//tNdhnyu9hFdvcq7hAuup27+KkUNt8+ZqoaNafiJb2mLSOey49BiWFkZRbxOr+uUoQb62h7+aLt5yKP98wMaOMbOKNaEWMw/qWZGyzypIn6vPdFx+NcUP64IyxmQ/ExBRy3fFI3/yagGj+xFEDe1n22w/MfTcLrpcHhT5nd9jw9j4k2ZeNyTCC9uyb5fnpo2aMjQIwEUDGktyMsTsYYxWMsYra2sxZeaqs2nUQt7zwOa5/dhHOf3yu63pUeHFhZcY2K6EuLoimoiCumZj5nNJ803Y/OrOoiGhuk6/fdu3Jw7H+N5faJsz/8cXjsPL+i/H8N8sx+0fmCSSJ9ieNGoBzxw3GlScNSz1sNGTJjkTJn56/+VSMGWQUSQbxNRH1/JjDSvHBD89GadKNlInJR22aQq4Jd7+ehXj4mhMs++4V28FERUkT1XNlcmBZZXA6s91M0pONHFeXWX8e+6jFk1wULOosDIKqoCzUjLHeAN4E8APOeYN5P+f8Wc55Oee8vKyszHWHDhxKW7jNgnhhp+yob8HaqozuWtKjSDwYWFwQScUqi9wbfRRcHwDQt2dChAZJBryabSxqDTvfbyTCUFpSiPOPGZKxlJbKD9cclfCH609KTaEWTR8fXFqS8RCzzEFtiPpQiKPmmXVpr6Xadp5yhTjPleInXgYTGQOevekUfPDDs/Gbq4932G6IfdQhsUyB9G9fJUokLGGFSkmPGWOFSIj0VM759GC75B+dcY6zH5sDAPh/XxqndExPi+WsCqIsZVGLokD69ki4Iex8cRePH4LHv3oSrjzJev295jZFoU7+7+YGSv1IdceaHzJmi/2aicPR2Jromzkhk0ZRQeazX+QnNU54UcN8mvrwPEAfVy0oG+D9luEKEXwfhVGWkaNcGDnDgYuTq+D4Gb3nhz88qPC8XKHy8JCvmZg9VKI+GIDnAKzjnD8RfJf844UF2zK26Z+QojAukdAAQGE0ktonWhTguGGlAIBhAj+tHsYYrjtluNTf/T1T5IkVbl8n5/3kvNR1iMiEWrDEVWHSHdIRE7d98xmj8O2zx6TqNeTnMPmYnZKZ5tQ44SVtYXu3qGXH24bnCfaLvm+/XCiq9XnFi8UelpwZQFp87R4e+RZHfSaAmwCczxhbnvx3WcD98kzVgUN4cEZm+lL9dRdlcLMaQCvUWdQi/+z4YaV4/66z8PK3MmebTRzZD7+4/Filfp9zdBmG9cucvCLCbFGqMmJAz9TBejEwD4SKfOBa8qd2i/wnJYVR3HvZseiVdCHp05HqOeuotHtM5V7g4JYWprZdu6kSM8qDUy27yy3qZ4nDXCwq7ajg5a3LjBcLPyR6Z0Ap6iMk/bZ1fXDO5yN36QtcwTnHr99Zo1TOjJVQF0QiqVjpcYf1Qa/iAsxYWY2+PQox76fnpQbAmkxui+e/WY7zjxGnMzVz9JDeeOyrJyqV1fffzU2onYt+QVrz5RDNnNMeVnYpTg2uDcFDYdSgXrjvivF44N21SmldEz5qo3VuzsqXngCTax+1mkVth1NhDHMcdVhyZgA6H7VdOW7X7+x13PnCfHnAjFXV+GDNXttyIqvQ2qKO4OunjkBtQyu+fc6R6FVcgJ9ddgi9iwoMUQrm1UZURRoA7jx3LAb3kbtO9IwbUor3Vu3BYaXqx2icMLwv/u+mU3DO0ZkDv8cfXorVuxsyokCAtOvDyqLWEE1f9yqep47qj93LD6X+1ixo7TvTu3OOP7yvt8Yk2J2GaL/T7IaJerqS68PHjviEVx91NumSQr29vkWpnMiFYeVGKCxgKIxGcPfF6UHJwwUuCn1eaNlMRj3pmVLOfhXfP38sphw1CKcc0V+p/LTbJxt88F9KDlqZeeqGk1HX1CZ0DU1MJpG6YZJ8hRjtOuotXzNOXss5gEe+ciIKohG8sXQXmG7NxLTrI932sUNLse6BS3Dby59jweZ6+wZskPus7cuKLGo7EQhZrimPg4m5VTxRHLVdZghuE0edzTPqckJd09AqzHanfTla1AKQGBA7aUQ//P6rJ+KzLfXoXVJgKa6FgoE1EXqrY/HP7FdaAdLuB5UE+HqiEaYs0oB6PuG+PQoxapB40siQ0hJUPnK5bR3aVbCa8AJkDgaa6V1cYHAllRRG8Z1zxuCNpbtwxUlDMXdjjaGNuMkVZJ5l6gSzNTvnR+em99kNAgoKDOhlFRvurB5pecE2PzIXanjL9eG9fS+4j6MOh0ndpYR6X3M7Jj08W7hva20zAOAfi7bjN1cfjyc+2og9Da24cPxgjB3cB2MHp9N1vvP9KZi5php/mbMFg3oXoa6pHccOLQ2s33ddeBQmjOgndEPkgkKLyBcnaCLDYP2mkBJWizoW/+wCTFuyAw/OWJe60ccO7pN+UKQsaK0+Y9t+EWGwfHCp8MfrJ2DOhszUBfaTo5y1E+Z81Lme8AJk9l8ljjosE166lFA//uEGy33Tv9id+vx6xU48OXsTALEf8IThfbG2+iAA4L8mjcTFxx0WqM+zMBrBhRbrJ+YCP1b1Fk5qtLhRrASgV3FBKiuhSOzNUS+aGIiSUXmZuJAp/My0X378ccNKhUJt367T8sEqdVfJ9eHE1RiC5wuALiTUdU1teHXxDqWyP3ljZepz9cFDwjLXnjwcBw914MqThglzPXdlVN08MvQPQDsftUwApImlMuKoM1/zXUdCeIz5NlQlmIADqGZvc9COs+JZJSwuBD22cdR2UR9Z9FJ3GaFeYLOSOJBYBcWchMnKUi6MRnDH2Uf60rd8Q7bggHIdySo4EpYxkI4Y0Uj7lN21Zx6MFAm/HzeTuXtOfd9Rlw8+P7TNTynpMhZ18qqQjzrL7G9ux12vLbctd1hpCR6+5ng0HIrha6eOwM59LSgLOMl8d4XprNzHrjsR05bsQLlp4NNRwiDB/WIOz4tL6vMSY2w+9vB+PfDX/z4ZS7fvx9/nb7Ot260rybFISJrxQ288+ahDkjNDj53fPBH1kaXO2BA6oXbzg/rX0p1K5XoWRXHJ8ekcGyN0kz0Ib2i+ZA3NiOQ8MQP0++cflXGM5qqQGfDaLuGofTK8yuyjFll+qkLx3M3l6FNSKB3vAIBLTxiKzTVNSnUWSbIQynB6KwQ94SWfoz70pHzUSjNi3e70l9AtxeX03NtjcTz83nppGS3XcolFwiUiwcu3TsJ3z3Xu7pnz43Mx58fnGrappHNNuS4kAqOiDZrQf3nCMIwd3BvfPGNU+niH4nXBsUMwafQAUyccVZFBYTRimYBJimn/RMFCyHrCHPUhW+ElG4i67tVHnU1CZ1E7fd2zGgzUOOWI/qlYYy1FZ9BMve00V7kdcs3ZR5fhbBchgqMFoWvajSEValN4nQzRDcNNPu7BfUow6+5zpPUs++VFiNnMqjTjVf+s8obbWfnm/a/eNhnH3jfTUdt+6oyXoYswuBDMS3B59VF36wkvTp68dU1t+NOsTZb7Txs9AK/dMRmMMaVJGn5x5thBWWsrrKQtausycQUntcyKSw8e2vdHa0q0WLCwXYU+qP5SC6ORDLF/4Zun2h5n1girzI4assvgj2B7GUzMrVK7nvDi7JkeGKEz+5w8eb/x3BJDfDRg9JX+89unZ3+hUwJAOnJEJamNW0tNn4TJimx8/XZtmKNdehVFcd4xg23rNV852xwjwgLeBdLJm08+kPpJKvmo7d8Is0EIhVrt7LfUNmFtdebKLWHxKXV3tDUhZVE1Kj5qc1k95qgP4XF+RDtY9E+17qhpJQPV8Edz/XYPhKB/+kHlo84VKj7qMLhsgDx2fWiTW846ahBeumUSKrbvRzTCMGvdXvx17hYsuveCILtJ2HDbWaNx65TRSiIqj/pghrKG47UyCvrhxbK2S8PqtOqIOfDbAqfiZrcMnFe8+ahDonhwFkdNE14sUPmtHWhpx7+/2I0vHTcE/3dTOQCkRupPOaI/fnTR0dKFWYngYYzBLnzYnERJXI/1PrukTsaytkUssVtE2CkRNZ3OdH3YnKdo5aF0XT5M/PHko/bcvO/YCXWY4qhDp2bmVUZEPL+gEvtb2vGdc8ShZCTS+YHXJErZ8lGLliQD3IufykIJiQbS9T9yrf2q6p2CkS8/Ddl8T8qk4SiOOiT9Dp2i2V2YtlgnXl28HeeNG4yJI/tLyxLhRhM6mQBoS3r175mZJtRJ1IdTjjksnU2xyM6iVlAw49qRaj51vTXXU7CIg5lY8oD/PX8sBpqiW3I9MzHX0RPiXCsq4XnW+2gwUcI7K6pR19SOW84clZ0OEcGhYBFfcOxg/Oaq43DPpZlrTprjqP3kZ5cfi19dOR6AQtpXh3eslt3PPs0mF362QsvDPrRfD5w6aoBNaedo35PyG4GOMPmoNWwXDgjRhJfQCbVsLgLnHC8s2IajBvfGFIpVznvs8lEDCRG+6fRRwkRIjuKoHfatuCCKyWMSCy2I1o5UQR/xon+WKHs+HLanWdQiIfVDbrRzcHM5ci13ruOoZRa1++44JoSDidan/8XOA1hT1YAHrz6e4qO7AHEFi1p6vESYVHjxllNR29hmXX/yt2iOg87Aov9zfnwu2jo6BcXdhefZofmo9Q8Wt2ISjbCMKBLte0r876zmMFnUqaW47N5oEJ5kUuETasnVm7Z4B3oWRXH1xMOz2CMiKBxlz5Mer+IjzuTccfJJJ5orwUqozdrzzTNG4d2VVam/excXCBcITiWsshEBp+KmWdQF0YjnQdQIA8yPGJba57zyEOm0Dm8zE7PpFgmd68NKpxtaO/DOyipcNWGY8MdP5B9+56P2m5hmodoMJmp77//ycaj4xUW29UYUfdR6VMpqDxa3rho9QjFObsp3H7XWFfsJL/LFbbNJ6BTP6sK8tbwKrR1x3DApO4mViOzhVla4go87VdZF/R02FrUT9H0ULRUmQn8rqLyCS33UDgVHmCrWwxtQWOKR9diJ8E/fXImNe61T2YYq6oMx9jxjrIYxtjobHRJdPM45pi3egfFDS3FCgGsXEtlF+65d5/pI/h/UeEVHcmTbKvG/2/tUtbtO/aOaj9qfNS8z61CZsm9FWKInAH32PHk5mUhnGxVT4UUAlwTcjxQiH/Wq3QextroBN5w2kgYRuxCpCSsulTroZEFpV4JN1jqH7asKnUzbHv/qSRnb0hZ1ur/m1J6qiLqoDS7mo49aGEed6045wNb1wTn/lDE2Kgt9wZV/no/qg62GbRc98Ql2HziEHoVRXDVhWDa6QWQJzaXg1rXQoyiKQx2d0qnNxQWJsD5Vd4MIqzERbSKMSv+LdfnJeyQn8YgEW99N/X6zOF53ynD8+F8rTP3RridLLZKhdc2puPYuLkBDawxAYmWktlh6VK1XcRT7mh1Vh0821iqXLYpG0O4wZ7gdNY1t+HDNHgDAiwsr8c6KKjS0dniq86bnFmd89/17FuH175zuqV4RvvmoGWN3ALgDAEaOdOdHPrKsF0YM6IF5m+pQWlKIUYN6om+PQhw1pDeunTgcpSWZs9OI/OWHFx2FwgKGr5w83NXxr3/7dMxet1e62OwjXzkBLyzojTOOHOi4/rOPLsN3zz0St581Rrj/W1PGoLE1hm9NGW1b108uOQa9igtQGIngv5ILWJw+ZiBuP2s09jV34M7zjsRby6tw3LDS1DE3Tj4Cm2uaUFwQweUnJJaQu++K8Tg9eS6vf/t0bK9vRklhFH17FOKYoX3w8sLtmDx6IMYPLcVhfUtw4bFDAACjBvbE3RcdjaOH9EFNYys27GnE1MU7cHi/Hrh1ymgM6FWI6ct24+LxQ9DQGsPlJwzFwi31OHZoH/QpKcTsdXsxvH9P/L8vjcPlJwxFXVMbttY2o3dJAXoWRbFk2z6srmrAMYf1Qe/iAnAOjBrUE4u21mNfczuiEYYR/Xuif68izFq7F4NLi3HKEQPwm3fX4rHrTsSxQ0vx10+24Lxxg3HC4X0xb1Mtxh3WB796ew0AYGjfEmyuacJVEw7Hx+trcKClHV8rH4HK+mYcaOnA+KGlqGlsQ01jK6oOtGLiyH4o612Mv8/fhp5FUUwZOwgFUYZ5m+oweUx6MtDS7fsx7rBSLK3ch1NHD8C66gaMHdwb2+tb0KekEBEGTBk7CDv2tWDOhhr0Li7EyAE90NAaw9FDemd8z0FpFFMx/5MW9buc8+NVKi0vL+cVFRUeu0YQBNF9YIwt5ZyXi/aFLjyPIAiCMEJCTRAEEXJUwvOmAfgMwDjG2C7G2LeC7xZBEAShoRL1cUM2OkIQBEGIIdcHQRBEyCGhJgiCCDkk1ARBECGHhJogCCLkKE14cVwpY7UAtrs8fBCAOh+7kw90t3PubucL0Dl3F7yc8xGc8zLRjkCE2guMsQqr2Tldle52zt3tfAE65+5CUOdMrg+CIIiQQ0JNEAQRcsIo1M/mugM5oLudc3c7X4DOubsQyDmHzkdNEARBGAmjRU0QBEHoIKEmCIIIOaERasbYJYyxDYyxzYyxe3LdH79gjI1gjM1hjK1jjK1hjN2V3D6AMfYRY2xT8v/+umPuTV6HDYyxL+Wu9+5hjEUZY18wxt5N/t3Vz7cfY+wNxtj65Hd9ejc45x8mf9OrGWPTGGMlXe2cRYt7uzlHxtgpjLFVyX1PMqeLv3LOc/4PQBTAFgBjABQBWAFgfK775dO5DQVwcvJzHwAbAYwH8CiAe5Lb7wHwu+Tn8cnzLwYwOnldork+DxfnfTeAV5FYGQjd4HxfAnBb8nMRgH5d+ZwBHA5gG4Aeyb9fB/DNrnbOAM4GcDKA1bptjs8RwBIApyOxzu77AC510o+wWNSTAGzmnG/lnLcDeA3AVTnuky9wzqs558uSnxsBrEPiR34VEjc3kv9fnfx8FYDXOOdtnPNtADYjcX3yBsbYcACXA/i7bnNXPt9SJG7o5wCAc97OOT+ALnzOSQoA9GCMFQDoCaAKXeycOeefAthn2uzoHBljQwGUcs4/4wnVfll3jBJhEerDAezU/b0rua1LkVx7ciKAxQCGcM6rgYSYAxicLNYVrsUfAfwEgH4p6a58vmMA1AJ4Ienu+TtjrBe68DlzzncDeBzADgDVAA5yzj9EFz5nHU7P8fDkZ/N2ZcIi1CJ/TZeKG2SM9QbwJoAfcM4bZEUF2/LmWjDGrgBQwzlfqnqIYFvenG+SAiRej//KOZ8IoBmJV2Ir8v6ck37Zq5B4xR8GoBdj7EbZIYJteXXOClido+dzD4tQ7wIwQvf3cCReo7oEjLFCJER6Kud8enLz3uQrEZL/1yS35/u1OBPAlxljlUi4sM5njL2Crnu+QOIcdnHOFyf/fgMJ4e7K53whgG2c81rOeQeA6QDOQNc+Zw2n57gr+dm8XZmwCPXnAI5ijI1mjBUB+DqAt3PcJ19Iju4+B2Ad5/wJ3a63Adyc/HwzgLd027/OGCtmjI0GcBQSAxF5Aef8Xs75cM75KCS+x4855zeii54vAHDO9wDYyRgbl9x0AYC16MLnjITLYzJjrGfyN34BEuMvXfmcNRydY9I90sgYm5y8Vt/QHaNGrkdVdSOplyEREbEFwM9z3R8fz2sKEq85KwEsT/67DMBAALMBbEr+P0B3zM+T12EDHI4Oh+kfgHORjvro0ucLYAKAiuT3/B8A/bvBOf8awHoAqwH8A4lohy51zgCmIeGD70DCMv6Wm3MEUJ68TlsAPIXkrHDVfzSFnCAIIuSExfVBEARBWEBCTRAEEXJIqAmCIEIOCTVBEETIIaEmCIIIOSTUBEEQIYeEmiAIIuT8fxUXCci1S3BDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count= 90\n",
      "54.88 %\n"
     ]
    },
    {
     "data": {
      "image/png": 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O+v4d4PPA/cCfMHh3R1N9A+9n8BrB1xmcab/xbHoE5rvn6SHgFrpP9k+6+dF/SWrEWrvkIklagYEuSY0w0CWpEQa6JDXCQJekRhjoktQIA12SGvG/w7dxMkwMUsEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fin\n"
     ]
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import sympy\n",
    "import math\n",
    "from random import randint\n",
    "\n",
    "def Exp(N,expN):\n",
    "    if N>10:\n",
    "        pi=2*N**0.5/math.log(N)\n",
    "        r=randint(5,N)\n",
    "        if r==N:\n",
    "            r=N-2\n",
    "        s=N-r\n",
    "        if r<=10:\n",
    "            er=expN[r]    \n",
    "        else:\n",
    "            expN[N]=max(pi-expN[r]-expN[s],expN[N])\n",
    "        if s<=10:\n",
    "            es=expN[s]\n",
    "        else:\n",
    "            expN[N]=max(pi-expN[r]-expN[s],expN[N])\n",
    "        return expN[N],expN\n",
    "    else:\n",
    "        return expN[N],expN\n",
    "\n",
    "n_iter=10\n",
    "Nmax=1000\n",
    "primes=list(sympy.primerange(2,Nmax+1))\n",
    "prime_train=[2,3,5,7]\n",
    "expN=[1]*(Nmax+2)\n",
    "expN[2]=1\n",
    "expN[3]=1\n",
    "expN[4]=1\n",
    "expN[5]=1\n",
    "expN[6]=2\n",
    "expN[7]=1\n",
    "expN[8]=1\n",
    "expN[9]=1\n",
    "expN[10]=2\n",
    "\n",
    "PrimeTrue=[]\n",
    "PrimeCheck=[]\n",
    "for n in range(10,Nmax+1):\n",
    "    BOOL=True\n",
    "    if n in primes:\n",
    "        PrimeTrue.append(1)\n",
    "    else:\n",
    "        PrimeTrue.append(0)\n",
    "    pi=2*n**0.5/math.log(n)\n",
    "    \n",
    "    for m in range(n_iter):\n",
    "        r=randint(5,n)\n",
    "        if r==n:\n",
    "            r=n-2\n",
    "        s=n-r\n",
    "        g=math.gcd(s,r)\n",
    "        if g!=1:\n",
    "            PrimeCheck.append(0)\n",
    "            break\n",
    "        else:\n",
    "            if m==0:\n",
    "                ermax,expN=Exp(r,expN)\n",
    "                esmax,expN=Exp(s,expN)\n",
    "            else:\n",
    "                er,expN=Exp(r,expN)\n",
    "                es,expN=Exp(s,expN)\n",
    "                ermax=max(er,ermax)\n",
    "                esmax=max(es,esmax)\n",
    "            prob=(ermax+esmax)/pi\n",
    "    if prob >0.5:\n",
    "        PrimeCheck.append(1)\n",
    "    else:\n",
    "        PrimeCheck.append(0)\n",
    "\n",
    "x=[]\n",
    "Hit=[]\n",
    "count=0\n",
    "for n in range(Nmax-10):\n",
    "    C=PrimeCheck[n]\n",
    "    T=PrimeTrue[n]\n",
    "    if C==T:\n",
    "        count+=1\n",
    "        x.append(n)\n",
    "        Hit.append(1)\n",
    "    else:\n",
    "        x.append(n)\n",
    "        Hit.append(0)\n",
    "\n",
    "print('count=',count)\n",
    "print(round(count/Nmax*100,2),'%')\n",
    "\n",
    "plt.bar(x,Hit)\n",
    "plt.show()\n",
    "plt.plot(expN)\n",
    "plt.show()\n",
    "\n",
    "\n",
    "count=0\n",
    "for n in range(Nmax-10):\n",
    "    C=PrimeCheck[n]\n",
    "    T=PrimeTrue[n]\n",
    "    if C==T and T==1:\n",
    "        count+=1\n",
    "        x.append(n)\n",
    "        Hit.append(1)\n",
    "    else:\n",
    "        x.append(n)\n",
    "        Hit.append(0)\n",
    "\n",
    "print('count=',count)\n",
    "print(round(count/(len(primes)-4)*100,2),'%')\n",
    "\n",
    "plt.bar(x,Hit)\n",
    "plt.show()\n",
    "\n",
    "print('Fin')"
   ]
  }
 ],
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