Statistics

Problem Statement for "StrongPrimePower"

Problem Statement

NOTE: This problem statement contains superscripts that may not display properly if viewed outside of the applet.

A number which can be represented as pq, where p is a prime number and q is an integer greater than 0, is called a prime power. If q is larger than 1, we call the number a strong prime power. You are given an integer n. If n is a strong prime power, return an int[] containing exactly two elements. The first element is p and the second element is q. If n is not a strong prime power, return an empty int[].

Definition

Class:
StrongPrimePower
Method:
baseAndExponent
Parameters:
String
Returns:
int[]
Method signature:
int[] baseAndExponent(String n)
(be sure your method is public)

Constraints

  • n will contain digits ('0' - '9') only.
  • n will represent an integer between 2 and 10^18, inclusive.
  • n will have no leading zeros.

Examples

  1. "27"

    Returns: {3, 3 }

    27 = 33. This is a strong prime power.

  2. "10"

    Returns: { }

    10 = 2 * 5. This is not a strong prime power.

  3. "7"

    Returns: { }

    A prime number is not a strong prime power.

  4. "1296"

    Returns: { }

  5. "576460752303423488"

    Returns: {2, 59 }

  6. "999999874000003969"

    Returns: {999999937, 2 }

  7. "828100056420000961"

    Returns: {910000031, 2 }

  8. "846400038640000441"

    Returns: {920000021, 2 }

  9. "864900031620000289"

    Returns: {930000017, 2 }

  10. "883600005640000009"

    Returns: {940000003, 2 }

  11. "640000017600000121"

    Returns: {800000011, 2 }

  12. "490000001400000001"

    Returns: {700000001, 2 }

  13. "4808584372417849"

    Returns: {37, 10 }

  14. "100"

    Returns: { }

  15. "10000000000000000"

    Returns: { }

  16. "576460752303423488"

    Returns: {2, 59 }

  17. "285311670611"

    Returns: {11, 11 }

  18. "3656158440062976"

    Returns: { }

  19. "128"

    Returns: {2, 7 }

  20. "2000"

    Returns: { }

  21. "81"

    Returns: {3, 4 }

  22. "1000000000000000000"

    Returns: { }

  23. "94931877133"

    Returns: {37, 7 }

  24. "625"

    Returns: {5, 4 }

  25. "1000000000000"

    Returns: { }

  26. "25937424601"

    Returns: {11, 10 }

  27. "64004320097200729"

    Returns: {400009, 3 }

  28. "6226558992207611"

    Returns: {183971, 3 }

  29. "450283905890997363"

    Returns: {3, 37 }

  30. "59604644775390625"

    Returns: {5, 24 }

  31. "79792266297612001"

    Returns: {7, 20 }

  32. "45949729863572161"

    Returns: {11, 16 }

  33. "51185893014090757"

    Returns: {13, 15 }

  34. "9904578032905937"

    Returns: {17, 13 }

  35. "2213314919066161"

    Returns: {19, 12 }

  36. "952809757913927"

    Returns: {23, 11 }

  37. "420707233300201"

    Returns: {29, 10 }

  38. "2141202151369"

    Returns: {12889, 3 }

  39. "5228251023757481"

    Returns: {173561, 3 }

  40. "149459220327509"

    Returns: {53069, 3 }

  41. "26293188972239280"

    Returns: { }

  42. "1737651513529567"

    Returns: {120223, 3 }

  43. "5272294069201823"

    Returns: {174047, 3 }

  44. "10885107702466060"

    Returns: { }

  45. "473820471009858816"

    Returns: { }

  46. "34744587261921628"

    Returns: { }

  47. "59354142037386528"

    Returns: { }

  48. "127303403660161"

    Returns: {3359, 4 }

  49. "165214544934378240"

    Returns: { }

  50. "450194580074537280"

    Returns: { }

  51. "98795453716788480"

    Returns: { }

  52. "7648371893761"

    Returns: {1663, 4 }

  53. "18113272128961"

    Returns: {2063, 4 }

  54. "1302058592234401"

    Returns: {6007, 4 }

  55. "38011495109306160"

    Returns: { }

  56. "178096532776492800"

    Returns: { }

  57. "141202341361"

    Returns: {613, 4 }

  58. "719112708318707456"

    Returns: { }

  59. "982451233759284608"

    Returns: { }

  60. "132421277116505056"

    Returns: { }

  61. "1164912556234151"

    Returns: {1031, 5 }

  62. "1258284197543"

    Returns: {263, 5 }

  63. "116771555364833952"

    Returns: { }

  64. "3973195810651"

    Returns: {331, 5 }

  65. "162198112382958592"

    Returns: { }

  66. "44567945135334456"

    Returns: { }

  67. "69693216111707"

    Returns: {587, 5 }

  68. "70675003317157848"

    Returns: { }

  69. "179407098289692000"

    Returns: { }

  70. "10942526586601"

    Returns: {149, 6 }

  71. "69366243661827840"

    Returns: { }

  72. "1745729089577929"

    Returns: {347, 6 }

  73. "136821750708889"

    Returns: {227, 6 }

  74. "108859988535875648"

    Returns: { }

  75. "1315127813325481"

    Returns: {331, 6 }

  76. "280343912229566656"

    Returns: { }

  77. "487014306255994624"

    Returns: { }

  78. "18619893262512572"

    Returns: { }

  79. "17249876309"

    Returns: {29, 7 }

  80. "9095120158391"

    Returns: {71, 7 }

  81. "435307306210734208"

    Returns: { }

  82. "605767994083541376"

    Returns: { }

  83. "321673167473963584"

    Returns: { }

  84. "80798284478113"

    Returns: {97, 7 }

  85. "27136050989627"

    Returns: {83, 7 }

  86. "12667700813876160"

    Returns: { }

  87. "124097929967680320"

    Returns: { }

  88. "67675234241018880"

    Returns: { }

  89. "7984925229121"

    Returns: {41, 8 }

  90. "139353667211683680"

    Returns: { }

  91. "406067677556641"

    Returns: {67, 8 }

  92. "16983563041"

    Returns: {19, 8 }

  93. "7837433594376961"

    Returns: {97, 8 }

  94. "806460091894081"

    Returns: {73, 8 }

  95. "118587876497"

    Returns: {17, 9 }

  96. "1119130473102767"

    Returns: {47, 9 }

  97. "760231058654565248"

    Returns: { }

  98. "3299763591802133"

    Returns: {53, 9 }

  99. "350356403707485184"

    Returns: { }

  100. "1024"

    Returns: {2, 10 }

  101. "13422659310152400"

    Returns: { }

  102. "9765625"

    Returns: {5, 10 }

  103. "25937424601"

    Returns: {11, 10 }

  104. "41426511213649"

    Returns: {23, 10 }

  105. "420707233300201"

    Returns: {29, 10 }

  106. "174887470365513056"

    Returns: { }

  107. "4808584372417849"

    Returns: {37, 10 }

  108. "978016874631664000"

    Returns: { }

  109. "929822258883628544"

    Returns: { }

  110. "964395528636563072"

    Returns: { }

  111. "394078969157856448"

    Returns: { }

  112. "908866107619817600"

    Returns: { }

  113. "991472143481970688"

    Returns: { }

  114. "4019123992303641"

    Returns: { }

  115. "344863682824507648"

    Returns: { }

  116. "997401841249600128"

    Returns: { }

  117. "111141909747036"

    Returns: { }

  118. "2"

    Returns: { }

  119. "3"

    Returns: { }

  120. "4"

    Returns: {2, 2 }

  121. "5"

    Returns: { }

  122. "6"

    Returns: { }

  123. "8"

    Returns: {2, 3 }

  124. "9"

    Returns: {3, 2 }

  125. "558545864083284007"

    Returns: {7, 21 }

  126. "505447028499293771"

    Returns: {11, 17 }

  127. "665416609183179841"

    Returns: {13, 16 }

  128. "168377826559400929"

    Returns: {17, 14 }

  129. "799006685782884121"

    Returns: {19, 14 }

  130. "576460752303423489"

    Returns: { }

  131. "576460752303423487"

    Returns: { }

  132. "450283905890997362"

    Returns: { }

  133. "450283905890997364"

    Returns: { }

  134. "298023223876953124"

    Returns: { }

  135. "298023223876953126"

    Returns: { }

  136. "558545864083284006"

    Returns: { }

  137. "558545864083284008"

    Returns: { }

  138. "505447028499293770"

    Returns: { }

  139. "505447028499293772"

    Returns: { }

  140. "665416609183179840"

    Returns: { }

  141. "665416609183179842"

    Returns: { }

  142. "168377826559400928"

    Returns: { }

  143. "168377826559400930"

    Returns: { }

  144. "799006685782884120"

    Returns: { }

  145. "799006685782884122"

    Returns: { }

  146. "999998384000652863"

    Returns: { }

  147. "999949000866995087"

    Returns: {999983, 3 }

  148. "982134461213542729"

    Returns: {997, 6 }

  149. "760231058654565217"

    Returns: {97, 9 }

  150. "5559060566555523"

    Returns: {3, 33 }

  151. "999999874000003968"

    Returns: { }

  152. "99999999999999997"

    Returns: { }

  153. "45848500718449031"

    Returns: {71, 9 }

  154. "417598221465052993"

    Returns: {747457, 3 }

  155. "999649041065398387"

    Returns: {999883, 3 }

  156. "999999874000003971"

    Returns: { }

  157. "99865325568854214"

    Returns: { }

  158. "16"

    Returns: {2, 4 }

  159. "639558602475808609"

    Returns: { }

  160. "61325611948023739"

    Returns: { }

  161. "999999874000003970"

    Returns: { }

  162. "999998274000744769"

    Returns: {999999137, 2 }

  163. "999999858000005041"

    Returns: {999999929, 2 }

  164. "998653255688542146"

    Returns: { }

  165. "6033563927688361"

    Returns: {77676019, 2 }

  166. "107213535210701"

    Returns: {101, 7 }

  167. "99999999"

    Returns: { }

  168. "362970615283037"

    Returns: {71333, 3 }

  169. "318632417065625869"

    Returns: { }

  170. "999999874000004021"

    Returns: { }

  171. "999999874000003999"

    Returns: { }

  172. "129961739795077"

    Returns: {37, 9 }

  173. "225"

    Returns: { }

  174. "26970310888669"

    Returns: {29989, 3 }

  175. "9999999999999999"

    Returns: { }

  176. "32212254719"

    Returns: { }

  177. "6975757441"

    Returns: {17, 8 }

  178. "40353607"

    Returns: {7, 9 }

  179. "18013367736991621"

    Returns: { }

  180. "999999999999999999"

    Returns: { }

  181. "256256096016001"

    Returns: {4001, 4 }

  182. "10828567056280801"

    Returns: {101, 8 }

  183. "999997000002999999"

    Returns: { }

  184. "45537538411"

    Returns: {3571, 3 }

  185. "64"

    Returns: {2, 6 }

  186. "999999999999999989"

    Returns: { }

  187. "8587340257"

    Returns: {97, 5 }

  188. "909090909090909091"

    Returns: { }

  189. "3534693810730681"

    Returns: {59453291, 2 }

  190. "999999786000011449"

    Returns: {999999893, 2 }

  191. "36028797018963967"

    Returns: { }

  192. "44373090883969"

    Returns: {6661313, 2 }

  193. "832972004929"

    Returns: {97, 6 }

  194. "125452795632756227"

    Returns: {500603, 3 }

  195. "288230376151711744"

    Returns: {2, 58 }

  196. "205891132094649"

    Returns: {3, 30 }

  197. "11398895185373143"

    Returns: {7, 19 }

  198. "94143178863"

    Returns: { }

  199. "1000002000001"

    Returns: { }

  200. "999999998000000001"

    Returns: { }

  201. "708362564245445649"

    Returns: { }

  202. "999999999999999967"

    Returns: { }

  203. "5014347704646281"

    Returns: {171161, 3 }

  204. "100000000000000"

    Returns: { }

  205. "809240558043136001"

    Returns: { }

  206. "1000030000300001"

    Returns: { }

  207. "36"

    Returns: { }

  208. "489061743789403"

    Returns: {78787, 3 }

  209. "2401"

    Returns: {7, 4 }

  210. "4220974735142131"

    Returns: {161611, 3 }

  211. "99420792564848581"

    Returns: {463261, 3 }

  212. "999999878000003721"

    Returns: { }

  213. "1002702430729"

    Returns: {10009, 3 }

  214. "1004536843742951"

    Returns: {100151, 3 }

  215. "63807265201"

    Returns: { }

  216. "513331712930412557"

    Returns: {800693, 3 }

  217. "991026973"

    Returns: {997, 3 }

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