If dP1, dP2, ........,dP24 are the difference between 24 prime numbers in series. 89 is the 24th Prime numbers Find the sum of dP1 + .... + dP24? (8th june Elitmus)
A) 85 B) 89 C) 95 D) 97

• 25 prime no.s b/n 1 & 100 are
  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
  
  difference b/n two primes
  dp1 =p2-p1= 3-2 =1
  dp2 =p3-p2= 5-3 =2
  ...
  dp24 = p25-p24 = 97-89 = 8
  
  1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8
  
  sum = dP1 + .... + dP24 = 95
• 10 years agoHelpfull: Yes(94) No(4)
• let dp1=p2-p1
  dp2=p3-p2....
  dp24=p25-p24
  so dp1+dp2+...dp24=p25-p1=97-2=95
• 10 years agoHelpfull: Yes(63) No(3)
• 25 prime no.s b/n 1 & 100 are
  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97
  
  difference between two prime number is...
  
  1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8
  
  sum = 1+ 2*8 + 4*7 + 7*6 +8 = 95
  
  
  
• 10 years agoHelpfull: Yes(14) No(0)
• hey, please discuss the skyscraper swaying problem as well
• 10 years agoHelpfull: Yes(4) No(0)
• gus wont the question be "If dP1, dP2, ........,dP24 are the difference between 25 prime numbers in series" --
• 10 years agoHelpfull: Yes(4) No(0)
• 2,3,5.........97 are the prime nos...
  then the sum of differences...
  (3-2)+(5-3)+(7-5)+(11-7)+(13-11)+........+(89-83)+(97-89)
  all terms cancels out except -2 and 97
  so ans 97-2 =95
  
• 9 years agoHelpfull: Yes(4) No(1)