giant prime

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Sidharth
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Joined:Sat Feb 08, 2014 11:29 pm
Location:Naogaon,Bangladesh
giant prime

Unread post by Sidharth » Tue Feb 11, 2014 12:21 am

একটি সংখ্যায় 119 টি 1 রয়েছে।প্রমাণ কর সংখ্যাটি মৌলিক নয়।

Tahmid
Posts:110
Joined:Wed Mar 20, 2013 10:50 pm

Re: giant prime

Unread post by Tahmid » Tue Feb 11, 2014 4:05 am

$111....1111$ [119, 1's]
$=10^{118}+10^{117}+10^{116}+......+10^{2}+10^{1}+10^{0}$
$=\frac{10^{119}-10^{0}}{10-1}$
$=\frac{(10^{7})^{17}-1^{17}}{9}$
$=\frac{(10^{7}-1)*(something)}{9}$
$=\frac{9999999*(something)}{9}$
$=1111111*(something)$

so, 111...111 [119, 1's] is a product of two integers. so it is not a prime. :)

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Labib
Posts:411
Joined:Thu Dec 09, 2010 10:58 pm
Location:Dhaka, Bangladesh.

Re: giant prime

Unread post by Labib » Tue Feb 11, 2014 11:28 pm

সংখ্যাতে 1 ছাড়া অন্য কোন অঙ্ক থাকতে পারবে না? (গঠন দেখে সেরকমই মনে হচ্ছে তবে স্টেটমেন্ট-এ পরিষ্কার বলা থাকলে ভাল হয়)
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Raiyan Jamil
Posts:138
Joined:Fri Mar 29, 2013 3:49 pm

Re: giant prime

Unread post by Raiyan Jamil » Wed Feb 12, 2014 10:19 am

111.....1111 (119 , 1's ) is not a prime because 119 is divisible by 17 and 7 . Now , let's try using another number . Like 111111111 . Here , as there are 9 , 1's and 9 is divisible by 3 , we can write it as 111*1001001 . Like this we can write 111...111 (119 , 1's) as 1111111*100000010000001.................10000001 . So , the number is not a prime .
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