{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Extracted Patterns: defaultdict(<class 'list'>, {'difference': [1, 2, 2, 6, 4, 2, 12, 30, 28, 18, 20, 394, 86, 672, 924], 'ratio': [1.5, 1.6666666666666667, 1.4, 1.8571428571428572, 1.3076923076923077, 1.1176470588235294, 1.631578947368421, 1.967741935483871, 1.459016393442623, 1.202247191011236, 1.1869158878504673, 4.102362204724409, 1.165067178502879, 2.1070840197693577, 1.7224394057857702]})\n",
      "Epoch 0/50, Loss: 96837.4922\n",
      "Epoch 10/50, Loss: 91576.0156\n",
      "Epoch 20/50, Loss: 86551.2422\n",
      "Epoch 30/50, Loss: 81648.4453\n",
      "Epoch 40/50, Loss: 76967.8594\n",
      "Predicted Next Mersenne Prime (Approx): 2551\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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aFIMGDdrjmNatW8fs2bPjK1/5Spx88skxevToaNeuXfzlL3+JX/7yl9GvX7+4+eab97iOpUuXxiWXXBLnnXdedO/ePXbu3Bnz5s2L8vLyOPfccyPi3Xfr06dPj6uuuirWrl0bI0eOjFatWsWaNWvinnvuiQsuuCCuuOKKA7bv71VWVha33357DBs2LHr27Bnnn39+dOrUKdatWxfLli2L1q1bx/33339Qtn0w3XLLLdG/f/+orKyMSZMmxdFHHx3r16+PJ598Mv7617/G888/v8f7P/roo/Hoo49GxLsv+Fu3bs1v3w8cODAGDhxYZ/ydd94ZO3fudOroIBCFA+Sss86KlStXxqxZs2LJkiXxk5/8JEqlUnTp0iXOOOOMuOiii+p8q3dflJWVxX333Rff+MY3Yv78+VEqlWLEiBExa9asOOmkk/Z7zj179ozHHnssrrrqqrj22mujpqYm+vbtG/Pnz9/n71wcKGPHjo1PfepTcd1118UNN9wQ27dvj06dOsWAAQPi/PPP3+v9e/XqFdXV1XH//ffHunXroqKiInr16hUPPvhgfPazn81xU6ZMie7du8ePfvSjmDZtWkS8+4HqkCFDDvrpiKqqqnjyySfjf/7nf+Lmm2+OLVu2RIcOHaJv375x4YUXHtRtHyw9evSIZ555JqZNmxZ33HFHbNy4Mdq3bx8nnXRSfO9739vr/ZcuXZrPQ63aD62nTp1aLwoLFiw4IKcZqc+/fQRA8pkCAEkUAEiiAEASBQCSKACQRAGA1OjvKTz77LMHcx58jBzM/78Z+Og05hsIjhQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQBIFAJIoAJBEAYAkCgAkUQAgiQIASRQASKIAQCoVRVE0amCpdLDnwsfEM88881FPgQ9Rnz59Puop8CFpzMu9IwUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEQBgCQKACRRACCJAgBJFABIogBAEgUAkigAkEpFURSNGlgqHey5AHAQNebl3pECAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGAJAoAJFEAIIkCAEkUAEiiAEBq0tiBRVEczHkA8DHgSAGAJAoAJFEAIIkCAEkUAEiiAEASBQCSKACQRAGA9L9Ntv0aZVlXIAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import networkx as nx\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "import torch.nn.functional as F\n",
    "from collections import defaultdict\n",
    "\n",
    "# Example known data for Mersenne primes and perfect numbers\n",
    "known_mersenne_primes = [2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203]\n",
    "known_perfect_numbers = [(2**(p - 1)) * (2**p - 1) for p in known_mersenne_primes]\n",
    "\n",
    "# Convert task ID or number to hexadecimal color for visualization\n",
    "def number_to_hex_color(number):\n",
    "    hex_str = f\"{hex(number)[2:]:0>6}\"  # Ensure it's 6 characters\n",
    "    return f\"#{hex_str[:6]}\"\n",
    "\n",
    "# Function to create graph from known numbers with color coding based on hex representation\n",
    "def create_graph(numbers):\n",
    "    G = nx.Graph()\n",
    "    for idx, num in enumerate(numbers):\n",
    "        # Convert the number to hex color for the node representation\n",
    "        hex_color = number_to_hex_color(num)\n",
    "        G.add_node(idx, value=num, color=hex_color)\n",
    "\n",
    "        # Connect each node to the previous node to show progression\n",
    "        if idx > 0:\n",
    "            G.add_edge(idx - 1, idx)\n",
    "\n",
    "    return G\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Updated function to visualize the graph with color-coding based on hexadecimal representation\n",
    "def visualize_graph(G, title=\"Number Graph\"):\n",
    "    pos = nx.spring_layout(G, seed=42)\n",
    "    node_colors = [G.nodes[node][\"color\"] for node in G.nodes()]\n",
    "    labels = {node: f\"{G.nodes[node]['value']}\\n{G.nodes[node]['color']}\" for node in G.nodes()}\n",
    "\n",
    "    fig, ax = plt.subplots(figsize=(10, 8))  # Explicitly create a figure and axis\n",
    "    nx.draw(\n",
    "        G, pos, labels=labels, node_color=node_colors, node_size=500, edgecolors=\"black\", ax=ax\n",
    "    )\n",
    "    ax.set_title(title)\n",
    "    plt.show()\n",
    "\n",
    "# Extract transformation patterns between numbers\n",
    "def extract_patterns(numbers):\n",
    "    patterns = defaultdict(list)\n",
    "    for i in range(1, len(numbers)):\n",
    "        # Calculate differences and ratios as potential patterns\n",
    "        diff = numbers[i] - numbers[i - 1]\n",
    "        ratio = numbers[i] / numbers[i - 1] if numbers[i - 1] != 0 else None\n",
    "        patterns[\"difference\"].append(diff)\n",
    "        patterns[\"ratio\"].append(ratio)\n",
    "\n",
    "    return patterns\n",
    "\n",
    "# Define a simple neural network model to learn from patterns\n",
    "class PatternModel(nn.Module):\n",
    "    def __init__(self):\n",
    "        super(PatternModel, self).__init__()\n",
    "        self.fc1 = nn.Linear(2, 16)\n",
    "        self.fc2 = nn.Linear(16, 16)\n",
    "        self.fc3 = nn.Linear(16, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = F.relu(self.fc1(x))\n",
    "        x = F.relu(self.fc2(x))\n",
    "        x = self.fc3(x)\n",
    "        return x\n",
    "\n",
    "# Train the model on the extracted patterns\n",
    "def train_model(model, patterns, epochs=100):\n",
    "    optimizer = torch.optim.Adam(model.parameters(), lr=0.001)\n",
    "    criterion = nn.MSELoss()\n",
    "\n",
    "    # Prepare data for training: differences and ratios\n",
    "    differences = torch.tensor(patterns[\"difference\"], dtype=torch.float32).unsqueeze(1)\n",
    "    ratios = torch.tensor(patterns[\"ratio\"], dtype=torch.float32).unsqueeze(1)\n",
    "    inputs = torch.cat((differences, ratios), dim=1)[:-1]\n",
    "    targets = differences[1:]  # Predict next difference\n",
    "\n",
    "    for epoch in range(epochs):\n",
    "        optimizer.zero_grad()\n",
    "        outputs = model(inputs)\n",
    "        loss = criterion(outputs, targets)\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        if epoch % 10 == 0:\n",
    "            print(f\"Epoch {epoch}/{epochs}, Loss: {loss.item():.4f}\")\n",
    "\n",
    "    return model\n",
    "\n",
    "# Predict the next number based on the last observed difference and ratio\n",
    "def predict_next_number(model, last_difference, last_ratio):\n",
    "    model.eval()\n",
    "    with torch.no_grad():\n",
    "        input_data = torch.tensor([[last_difference, last_ratio]], dtype=torch.float32)\n",
    "        next_difference = model(input_data).item()\n",
    "    return next_difference\n",
    "\n",
    "# Visualize grids based on numbers, simulating ARC-like grid representation\n",
    "def visualize_grid(grid, title=\"Number Grid\"):\n",
    "    plt.imshow(grid, cmap=\"nipy_spectral\", interpolation=\"nearest\")\n",
    "    plt.title(title)\n",
    "    plt.axis(\"off\")\n",
    "    plt.show()\n",
    "\n",
    "def number_to_grid(number):\n",
    "    binary_str = bin(number)[2:]\n",
    "    grid_size = int(np.ceil(np.sqrt(len(binary_str))))\n",
    "    grid = np.zeros((grid_size, grid_size), dtype=int)\n",
    "    for idx, bit in enumerate(binary_str):\n",
    "        grid[idx // grid_size][idx % grid_size] = int(bit)\n",
    "    return grid\n",
    "\n",
    "# Main function to run the updated process\n",
    "def main():\n",
    "    # Step 1: Create a graph for known Mersenne primes\n",
    "    G = create_graph(known_mersenne_primes)\n",
    "    visualize_graph(G, title=\"Mersenne Primes Graph\")\n",
    "    \n",
    "    # Step 2: Extract transformation patterns\n",
    "    patterns = extract_patterns(known_mersenne_primes)\n",
    "    print(\"Extracted Patterns:\", patterns)\n",
    "    \n",
    "    # Step 3: Train the model on the extracted patterns\n",
    "    model = PatternModel()\n",
    "    model = train_model(model, patterns, epochs=50)\n",
    "\n",
    "    # Step 4: Predict the next number\n",
    "    last_difference = patterns[\"difference\"][-1]\n",
    "    last_ratio = patterns[\"ratio\"][-1]\n",
    "    next_difference = predict_next_number(model, last_difference, last_ratio)\n",
    "    predicted_next_prime = known_mersenne_primes[-1] + next_difference\n",
    "    print(\"Predicted Next Mersenne Prime (Approx):\", int(predicted_next_prime))\n",
    "\n",
    "    # Step 5: Visualize the grid representation of each Mersenne prime\n",
    "    for num in known_mersenne_primes:\n",
    "        grid = number_to_grid(num)\n",
    "        visualize_grid(grid, title=f\"Grid for Mersenne Prime {num}\")\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    main()"
   ]
  }
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