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
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.
--------------------
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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Still searching (for many things, not least your palindromic prime) ...
––––––––––––––––––
Interesting question!
––––––––––––––––––
... 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)
––––––––––––––––––
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.
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