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# An interesting prime number

*especially for users of base-ten notation*

I saw the following number, allegedly prime, in the [twitter stream of Cliff Pickover](https://twitter.com/pickover/status/456534816335216640):

<img src="nines-prime.jpg" width="80%">

The number consists of 252 `9`'s, then a single digit `8`, then 253 `9`'s'

This file is a Sage worksheet with a brief calculation to confirm the number's primality.

 \- Hal Snyder

︡5eafd530-5657-414e-9207-01a4c5bc6959︡{"done":true,"md":"\n# An interesting prime number\n\n*especially for users of base-ten notation*\n\nI saw the following number, allegedly prime, in the [twitter stream of Cliff Pickover](https://twitter.com/pickover/status/456534816335216640):\n\n<img src=\"nines-prime.jpg\" width=\"80%\">\n\nThe number consists of 252 `9`'s, then a single digit `8`, then 253 `9`'s'\n\nThis file is a Sage worksheet with a brief calculation to confirm the number's primality.\n\n \\- Hal Snyder"}
︠aade49b2-3fee-4532-82da-888d35d3e6f1s︠
prefix_len = 3 * 74 + 30
suffix_len = 43 + 2 * 74 + 62
︡bd0fa15a-a43c-475f-8c0e-2f51d050fa45︡{"done":true}
︠3a6ce6f2-9ba9-436f-9762-f3fe1c9ee788s︠
seg_len = [prefix_len, 1, suffix_len]
seg_len
sum(seg_len)
︡3ceb2f9f-7e20-4532-8571-9d337b86db7f︡{"stdout":"[252, 1, 253]\n"}︡{"stdout":"506\n"}︡{"done":true}
︠cd2101d9-f6f0-4ac8-91c6-091b9db44cb7s︠
digits = ['9', '8', '9']
xstrs = [seg_len[k]*digits[k] for k in range(len(digs))]
xstr = ''.join(xstrs)
︡0e491742-45d0-4c4e-a6ea-ba06edc91fba︡{"done":true}
︠4459a7b1-4f54-491e-bce2-8b8464261a8d︠
xi = int(xstr)
factor(xi)
︡81f99408-3708-48b3-b1c7-dea4fd26b32c︡{"stdout":"99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999989999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999"}︡{"stdout":"\n"}︡{"done":true}
︠6b0978dc-521f-435b-998b-784180058130s︠
# how long does it take Sage to check that the number is prime?
%time is_prime(xi)

︡a6957fc3-053f-4af2-bd1f-c32f9584097a︡{"stdout":"True"}︡{"stdout":"\n"}︡{"stdout":"\nCPU time: 18.91 s, Wall time: 20.28 s\n"}︡{"done":true}
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