Curious properties of 11, 111, 1111, …

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Fun With Num3ers

Older post: Series of Num3ers 1111…


11 is a prime number.
111 = 3 * 37
1111 = 11 * 101
11111 = 41 * 271
…..
1111111111111111111 (19 digits) is a prime number.
11111111111111111111111 (23 digits) is a prime number.


Curious properties of 11:

(1)

1^2 = 1
11^2 = 121 1+2+1 = 4 = 2^2
111^2 = 12321 1+2+3+2+1 = 9 = 3^2
1111^2 = 1234321 1+2+3+4+3+2+1 = 16 = 4^2
11111^2 = 123454321 1+2+3+4+5+4+3+2+1 = 25 = 5^2
111111^2 = 12345654321 1+2+3+4+5+6+5+4+3+2+1 = 36 = 6^2
1111111^2 = 1234567654321 1+2+3+4+5+6+7+6+5+4+3+2+1 = 49 = 7^2
11111111^2 = 123456787654321 1+2+3+4+5+6+7+8+7+6+5+4+3+2+1 = 64 = 8^2

111111111^2 = 12345678987654321
1+2+3+4+5+6+7+8+9+8+7+6+5+4+3+2+1 = 81 = 9^2

1111111111^2 = 1234567900987654321
1+2+3+4+5+6+7+9+0+0+9+8+7+6+5+4+3+2+1 = 82 = 1^2 + 9^2

11111111111^2 = 123456790120987654321
1+2+3+4+5+6+7+9+0+1+2+0+9+8+7+6+5+4+3+2+1 = 85 = 2^2 + 9^2 = 6^2 + 7^2

111111111111^2 = 12345679012320987654321
1+2+3+4+5+6+7+9+0+1+2+3+2+0+9+8+7+6+5+4+3+2+1 = 90 = 3^2 + 9^2

1111111111111^2 = 1234567901234320987654321

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The Next Step

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Matrignosis: A Blog About Inner Wisdom

brain_power_large“Spirit and matter may well be forms of one and the same transcendental thing.” ~Carl Jung. CW 9i; par. 392.

This week between Christmas 2016 and the New Year of 2017 is the first in almost seven years that I didn’t schedule a Tuesday post on Matrignosis. I’m still trying to figure out why, but one factor is undoubtedly that I’m struggling with physical, emotional, and spiritual burnout from the presidential election and holiday preparations. As a result, I’m recovering from my second nasty bout with bronchitis in two months.

Determined to get the rest I obviously need this week, I had no conscious plans to write a post until after the new year. But this morning I awoke from a dream:

#4814 

A new government has taken over.  It is banning free speech and singling out intellectuals and other ‘undesirables’ on trumped up charges.  I’m feeling worried and…

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E.A. Bennet: Mrs. Jung died at 10.30 this morning. C.G. came up to the Niehus’s house to tell me and to say goodbye.

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Küsnacht, 23rd November 1955Arrived at Zürich station at 12.25 and was met by C.G. He told me Mrs. Jung was very ill and so I would not be staying with them but with his daughter Marianne Niehus. B…

Source: E.A. Bennet: Mrs. Jung died at 10.30 this morning. C.G. came up to the Niehus’s house to tell me and to say goodbye.