67 lines
1.8 KiB
Plaintext
67 lines
1.8 KiB
Plaintext
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"cell_type": "markdown",
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"source": [
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"# Spiral primes (Euler Problem 58)"
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]
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},
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"source": [
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"[https://projecteuler.net/problem=58](https://projecteuler.net/problem=58)\n",
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"\n",
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"Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.\n",
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"\n",
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"37 36 35 34 33 32 31\n",
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"38 17 16 15 14 13 30\n",
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"39 18 5 4 3 12 29\n",
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"40 19 6 1 2 11 28\n",
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"41 20 7 8 9 10 27\n",
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"42 21 22 23 24 25 26\n",
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"43 44 45 46 47 48 49\n",
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"\n",
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"It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 ≈ 62%.\n",
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"\n",
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"If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?"
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]
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},
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"display_name": "Python 3",
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"language": "python3.6",
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"version": "3.6.5"
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"tags": []
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