document.write( "Question 344030: HI! My question is: Can you find any numbers that are less than 300 and are divisible by four different prime numbers? If yes, generate all of them and explain how you know your list is complete. If no, explain why none exist. \n" ); document.write( "
Algebra.Com's Answer #246133 by CharlesG2(834)\"\" \"About 
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HI! My question is: Can you find any numbers that are less than 300 and are divisible by four different prime numbers? If yes, generate all of them and explain how you know your list is complete. If no, explain why none exist.\r
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\n" ); document.write( "\n" ); document.write( "list of prime numbers from 2 to 293 (between 0 and 50, 15 primes)
\n" ); document.write( "2 3 5 7 11 -------------------------------> 5 numbers
\n" ); document.write( "13 17 19 23 29 31 37 41 43 47 ------------> 10 numbers\r
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\n" ); document.write( "\n" ); document.write( "minimum product 4 primes: 2 * 3 * 5 * 7 = 6 * 5 * 7 = 30 * 7 = 210
\n" ); document.write( "next product 4 primes: 3 * 5 * 7 * 11 = 15 * 7 * 11 = 105 * 11 = 1155, too big
\n" ); document.write( "2 * 5 * 7 * 11 = 770, too big
\n" ); document.write( "minimum product of two 2-digit primes = 11 * 13 = 143, times 2 that is 286, times 3 it would be 429\r
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\n" ); document.write( "\n" ); document.write( "from what I can tell, there is only one number less than 300 that is product of 4 primes, and that is 210
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