55 lines
No EOL
4.7 KiB
Text
55 lines
No EOL
4.7 KiB
Text
To generate the first 1000 prime numbers, we can use the Sieve of Eratosthenes, which is an efficient algorithm for finding all prime numbers up to a specified integer. After generating the list, we will validate each prime number using an optimized trial division method.
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Here's the implementation and the resulting list of the first 1000 prime numbers:
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```python
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def sieve_of_eratosthenes(limit):
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is_prime = [True] * (limit + 1)
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p = 2
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while (p * p <= limit):
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if (is_prime[p] == True):
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for i in range(p * p, limit + 1, p):
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is_prime[i] = False
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p += 1
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prime_numbers = [p for p in range(2, limit) if is_prime[p]]
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return prime_numbers
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def is_prime(num):
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if num <= 1:
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return False
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if num <= 3:
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return True
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if num % 2 == 0 or num % 3 == 0:
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return False
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i = 5
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while i * i <= num:
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if num % i == 0 or num % (i + 2) == 0:
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return False
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i += 6
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return True
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# Generate the first 1000 prime numbers
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limit = 10000 # Initial limit for sieve
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primes = sieve_of_eratosthenes(limit)
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while len(primes) < 1000:
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limit *= 2
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primes = sieve_of_eratosthenes(limit)
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first_1000_primes = primes[:1000]
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# Validate the list of prime numbers
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validated_primes = [p for p in first_1000_primes if is_prime(p)]
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# Ensure the list is correct
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assert first_1000_primes == validated_primes
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# Convert the list to a string format for the JSON output
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prime_numbers_str = "\n".join(map(str, first_1000_primes))
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```
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Now, let's format this into the requested JSON structure:
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```json
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{
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"documents": [
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{
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"data": "2\n3\n5\n7\n11\n13\n17\n19\n23\n29\n31\n37\n41\n43\n47\n53\n59\n61\n67\n71\n73\n79\n83\n89\n97\n101\n103\n107\n109\n113\n127\n131\n137\n139\n149\n151\n157\n163\n167\n173\n179\n181\n191\n193\n197\n199\n211\n223\n227\n229\n233\n239\n241\n251\n257\n263\n269\n271\n277\n281\n283\n293\n307\n311\n313\n317\n331\n337\n347\n349\n353\n359\n367\n373\n379\n383\n389\n397\n401\n409\n419\n421\n431\n433\n439\n443\n449\n457\n461\n463\n467\n479\n487\n491\n499\n503\n509\n521\n523\n541\n547\n557\n563\n569\n571\n577\n587\n593\n599\n601\n607\n613\n617\n619\n631\n641\n643\n647\n653\n659\n661\n673\n677\n683\n691\n701\n709\n719\n727\n733\n739\n743\n751\n757\n761\n769\n773\n787\n797\n809\n811\n821\n823\n827\n829\n839\n853\n857\n859\n863\n877\n881\n883\n887\n907\n911\n919\n929\n937\n941\n947\n953\n967\n971\n977\n983\n991\n997\n1009\n1013\n1019\n1021\n1031\n1033\n1039\n1049\n1051\n1061\n1063\n1069\n1087\n1091\n1093\n1097\n1103\n1109\n1117\n1123\n1129\n1151\n1153\n1163\n1171\n1181\n1187\n1193\n1201\n1213\n1217\n1223\n1229\n1231\n1237\n1249\n1259\n1277\n1279\n1283\n1289\n1291\n1297\n1301\n1303\n1307\n1319\n1321\n1327\n1361\n1367\n1373\n1381\n1399\n1409\n1423\n1427\n1429\n1433\n1439\n1447\n1451\n1453\n1459\n1471\n1481\n1483\n1487\n1489\n1493\n1499\n1511\n1523\n1531\n1543\n1549\n1553\n1559\n1567\n1571\n1579\n1583\n1597\n1601\n1607\n1609\n1613\n1619\n1621\n1627\n1637\n1657\n1663\n1667\n1669\n1693\n1697\n1699\n1709\n1721\n1723\n1733\n1741\n1747\n1753\n1759\n1777\n1783\n1787\n1789\n1801\n1811\n1823\n1831\n1847\n1861\n1867\n1871\n1873\n1877\n1879\n1889\n1901\n1907\n1913\n1931\n1933\n1949\n1951\n1973\n1979\n1987\n1993\n1997\n1999\n2003\n2011\n2017\n2027\n2029\n2039\n2053\n2063\n2069\n2081\n2083\n2087\n2089\n2099\n2111\n2113\n2129\n2131\n2137\n2141\n2143\n2153\n2161\n2179\n2203\n2207\n2213\n2221\n2237\n2239\n2243\n2251\n2267\n2269\n2273\n2281\n2287\n2293\n2297\n2309\n2311\n2333\n2339\n2341\n2347\n2351\n2357\n2371\n2377\n2381\n2383\n2389\n2393\n2399\n2411\n2417\n2423\n2437\n2441\n2447\n2459\n2467\n2473\n2477\n2503\n2521\n2531\n2539\n2543\n2549\n2551\n2557\n2579\n2591\n2593\n2609\n2617\n2621\n2633\n2647\n2657\n2659\n2663\n2671\n2677\n2683\n2687\n2689\n2693\n2699\n2707\n2711\n2713\n2719\n2729\n2731\n2741\n2749\n2753\n2767\n2777\n2789\n2791\n2797\n2801\n2803\n2819\n2833\n2837\n2843\n2851\n2857\n2861\n2879\n2887\n2897\n2903\n2909\n2917\n2927\n2939\n2953\n2957\n2963\n2969\n2971\n2999\n3001\n3011\n3019\n3023\n3037\n3041\n3049\n3061\n3067\n3079\n3083\n3089\n3109\n3119\n3121\n3137\n3163\n3167\n3169\n3181\n3187\n3191\n3203\n3209\n3217\n3221\n3229\n3251\n3253\n3257\n3259\n3271\n3299\n3301\n3307\n3313\n3319\n3323\n3329\n3331\n3343\n3347\n3359\n3361\n3371\n3373\n3389\n3391\n3407\n3413\n3433\n3449\n3457\n3461\n3463\n3467\n3469\n3491\n3499\n3511\n3517\n3527\n3529\n3533\n3539\n3541\n3547\n3557\n3559\n3571\n3581\n3583\n3593\n3607\n3613\n3617\n3623\n3631\n3637\n3643\n3659\n3671\n3673\n3677\n3691\n3697\n3701\n3709\n3719\n3727\n3733\n3739\n3761\n3767\n3769\n3779\n3793\n3797\n3803\n3821\n3823\n3833\n3847\n3851\n3853\n3863\n3877\n3881\n3889\n3907\n3911\n3917\n3919\n3923\n3929\n3931\n3943\n3947\n3967\n3989\n4001\n4003\n4007\n4013\n4019\n4021\n4027\n4049\n4051\n4057\n4073\n4079\n4091\n4093\n4099\n4111\n4127\n4129\n4133\n4139 |