document.write( "Question 1194081: 99 consecutive natural numbers, all of which are composite.\r
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\n" ); document.write( "What is the largest number in this set? 100!+100\r
\n" ); document.write( "\n" ); document.write( "What is the method to calculate this? Are my answers correct? Thanks \n" ); document.write( "
Algebra.Com's Answer #826177 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "99 consecutive natural numbers, all of which are composite.
\n" ); document.write( "What is the smallest number in this set? 100!+2
\n" ); document.write( "What is the largest number in this set? 100!+100
\n" ); document.write( "What is the method to calculate this? Are my answers correct? Thanks
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\n" ); document.write( "\n" ); document.write( "            Your answers are incorrect.\r
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\n" ); document.write( "\n" ); document.write( "            I will construct a sequence of much smaller 99  consecutive natural number,  all of which are composite.\r
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document.write( "First consider all prime numbers lesser than 100:\r\n" );
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document.write( "    2, 3, 5, 7, 11, 13, 17, . . . , 89, 97.\r\n" );
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document.write( "Take each of them in maximum degree in a way it is still lesser tnan 100:\r\n" );
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document.write( "    2^6 = 64;  3^4 = 81;  5^2 = 25;  7^2 = 49;  11, 13, 17, . . . , 89, 97.\r\n" );
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document.write( "Take the product of these numbers\r\n" );
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document.write( "    N = \"2%5E6%2A3%5E4%2A5%5E2%2A7%5E2%2A11%2A13%2A17%2A+ellipsis+%2A+89%2A97\".\r\n" );
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document.write( "Then 99 consecutive natural numbers\r\n" );
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document.write( "    N+2, N+3, N+4, N+5, . . . , N+99, N+100\r\n" );
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document.write( "are \r\n" );
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document.write( "        (a)  all composite \r\n" );
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document.write( "    and \r\n" );
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document.write( "        (b)  these numbers are less than yours.\r\n" );
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document.write( "Notice, that I do not state that this sequence is minimal; but in any case, it is lesser than yours.\r\n" );
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