What is the first palindromic prime number above 100,000
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What is the first palindromic prime number above 100,000

[From: ] [author: ] [Date: 11-11-24] [Hit: ]
.. . . . .......
It won't be a 6-digit number:

abccba = a0000a + b00b0 + cc00
. . . . . . = 100001 a + 10010 b + 1100 c
. . . . . . = 11*9091a + 11*910b + 11*100c
. . . . . . = 11 (9091a + 910b + 100c)

So all palindromic 6-digit numbers are divisible by 11

You need to check 7-digit numbers.

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EDIT:

1101011 is not prime.
67 × 16433 = 1101011

1,000,001 = 101 × 9,901
1,001,001 = 3 x 333,667
1,002,001 = 7 x 143,143

1,003,001 ------> prime !

Smallest palindromic prime number above 100,000 is 1,003,001

Mαthmφm

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Unfortunately, 100,001 = 11 * 9091

Still searching (for many things, not least your palindromic prime) ...

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110,011 is also divisible by 11.

Interesting question!

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... and as a sideline, 11 and 101 are prime, but (interpolating zeros) is any number in the form 1001, 10001, 100001, 1000001, etc, prime?

(Not up to 10,000,000,000,000,000,001, which is 11 * 909,090,909,090,909,091)

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1101011 = 67 * 16433

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1003001 is prime ... just have to check whether it's the first > 100000

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Mαthmφm got there first.

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11*9091 = 100,001

FAIL To whoever said 100,001

Some nerd is going to have this fact totally memorized...I want to know the source of whoever gets it.

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100,001

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i thinks it's 100,001
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