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Problem Statement for "MagicStonesStore"

Problem Statement

Today is the Christmas Eve. People around the world celebrate this holiday. The following story takes place in the land of reindeer, where Santa Claus resides.


The currency in the land of reindeer are magic stones. Santa's reindeer have 2n magic stones (i.e., an even number of them). They want to divide the stones into two piggy banks. Santa's reindeer are very fond of primes, therefore they want each piggy bank to contain a prime number of magic stones.


You are given an int n. If it is possible to divide 2n magic stones into two piggy banks, each containing a prime number of stones, return "YES", otherwise return "NO" (quotes for clarity).

Definition

Class:
MagicStonesStore
Method:
ableToDivide
Parameters:
int
Returns:
String
Method signature:
String ableToDivide(int n)
(be sure your method is public)

Notes

  • A positive integer is prime if and only if it has exactly two positive integer divisors. The first few prime numbers are 2, 3, 5, 7, 11, ...
  • The number zero is not a prime number, hence you are not allowed to leave any piggy bank empty.

Constraints

  • n will be between 1 and 1,000, inclusive.

Examples

  1. 1

    Returns: "NO"

    As n=1, we are dividing 2 magic stones into two piggy banks. In this case is impossible to have a prime number of stones in each piggy bank.

  2. 2

    Returns: "YES"

    The only valid way of dividing the stones in this case is to put 2 magic stones into each of the piggy banks.

  3. 3

    Returns: "YES"

    Now the only way is to put 3 magic stones into each of the piggy banks.

  4. 5

    Returns: "YES"

    For 2n=10 stones we have two valid ways of dividing them: either as 5 + 5 or as 7 + 3.

  5. 1

    Returns: "NO"

  6. 2

    Returns: "YES"

  7. 3

    Returns: "YES"

  8. 4

    Returns: "YES"

  9. 5

    Returns: "YES"

  10. 6

    Returns: "YES"

  11. 7

    Returns: "YES"

  12. 8

    Returns: "YES"

  13. 9

    Returns: "YES"

  14. 10

    Returns: "YES"

  15. 1000

    Returns: "YES"

  16. 999

    Returns: "YES"

  17. 998

    Returns: "YES"

  18. 997

    Returns: "YES"

  19. 996

    Returns: "YES"

  20. 995

    Returns: "YES"

  21. 994

    Returns: "YES"

  22. 993

    Returns: "YES"

  23. 992

    Returns: "YES"

  24. 991

    Returns: "YES"

  25. 990

    Returns: "YES"

  26. 734

    Returns: "YES"

  27. 589

    Returns: "YES"

  28. 397

    Returns: "YES"

  29. 492

    Returns: "YES"

  30. 629

    Returns: "YES"

  31. 368

    Returns: "YES"

  32. 230

    Returns: "YES"

  33. 923

    Returns: "YES"

  34. 784

    Returns: "YES"

  35. 259

    Returns: "YES"

  36. 84

    Returns: "YES"

  37. 986

    Returns: "YES"

  38. 399

    Returns: "YES"

  39. 443

    Returns: "YES"

  40. 609

    Returns: "YES"

  41. 165

    Returns: "YES"

  42. 953

    Returns: "YES"

  43. 529

    Returns: "YES"

  44. 520

    Returns: "YES"

  45. 372

    Returns: "YES"

  46. 776

    Returns: "YES"

  47. 322

    Returns: "YES"

  48. 254

    Returns: "YES"

  49. 295

    Returns: "YES"

  50. 108

    Returns: "YES"

  51. 972

    Returns: "YES"

  52. 514

    Returns: "YES"

  53. 336

    Returns: "YES"

  54. 367

    Returns: "YES"

  55. 803

    Returns: "YES"

  56. 918

    Returns: "YES"

  57. 521

    Returns: "YES"

  58. 225

    Returns: "YES"

  59. 253

    Returns: "YES"

  60. 774

    Returns: "YES"

  61. 888

    Returns: "YES"

  62. 142

    Returns: "YES"

  63. 690

    Returns: "YES"

  64. 361

    Returns: "YES"

  65. 280

    Returns: "YES"

  66. 5

    Returns: "YES"

  67. 800

    Returns: "YES"

  68. 878

    Returns: "YES"

  69. 979

    Returns: "YES"

  70. 409

    Returns: "YES"

  71. 862

    Returns: "YES"

  72. 449

    Returns: "YES"

  73. 941

    Returns: "YES"

  74. 509

    Returns: "YES"

  75. 280

    Returns: "YES"

  76. 421

    Returns: "YES"

  77. 378

    Returns: "YES"

  78. 123

    Returns: "YES"

  79. 666

    Returns: "YES"

  80. 268

    Returns: "YES"

  81. 770

    Returns: "YES"

  82. 134

    Returns: "YES"

  83. 992

    Returns: "YES"

  84. 485

    Returns: "YES"

  85. 412

    Returns: "YES"

  86. 978

    Returns: "YES"

  87. 110

    Returns: "YES"

  88. 798

    Returns: "YES"

  89. 600

    Returns: "YES"

  90. 904

    Returns: "YES"

  91. 75

    Returns: "YES"

  92. 211

    Returns: "YES"

  93. 410

    Returns: "YES"

  94. 814

    Returns: "YES"

  95. 676

    Returns: "YES"

  96. 301

    Returns: "YES"

  97. 524

    Returns: "YES"

  98. 702

    Returns: "YES"

  99. 790

    Returns: "YES"

  100. 221

    Returns: "YES"

  101. 27

    Returns: "YES"

  102. 998

    Returns: "YES"

  103. 547

    Returns: "YES"

  104. 563

    Returns: "YES"

  105. 445

    Returns: "YES"

  106. 992

    Returns: "YES"

  107. 217

    Returns: "YES"

  108. 395

    Returns: "YES"

  109. 417

    Returns: "YES"

  110. 323

    Returns: "YES"

  111. 471

    Returns: "YES"

  112. 639

    Returns: "YES"

  113. 272

    Returns: "YES"

  114. 473

    Returns: "YES"

  115. 129

    Returns: "YES"

  116. 99

    Returns: "YES"

  117. 746

    Returns: "YES"

  118. 882

    Returns: "YES"

  119. 14

    Returns: "YES"

  120. 516

    Returns: "YES"

  121. 356

    Returns: "YES"

  122. 458

    Returns: "YES"

  123. 721

    Returns: "YES"

  124. 602

    Returns: "YES"

  125. 25

    Returns: "YES"

  126. 500

    Returns: "YES"

  127. 961

    Returns: "YES"

  128. 36

    Returns: "YES"

  129. 12

    Returns: "YES"

  130. 403

    Returns: "YES"

  131. 11

    Returns: "YES"

  132. 33

    Returns: "YES"

  133. 65

    Returns: "YES"

  134. 17

    Returns: "YES"

  135. 24

    Returns: "YES"

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