How-many-different-clock-type-dials-can-be-made-containing-first-n-natual-numbers-with-the-property-that-sum-of-any-two-numbers-of-consecutive-positions-be-a-prime-number-N-1-2-3-

FacebookTweetPin

Question Number 3172 by Rasheed Soomro last updated on 07/Dec/15

$$\mathcal{H}owmanydifferentclock-typedialscanbemade$$$$containingfirstnnatualnumberswiththeproperty$$$$thatsumofanytwonumbersofconsecutivepositionsbe$$$$aprimenumber.$$$$\mathbb{N}=\{1,2,3,\dots \}$$

Commented by Rasheed Soomro last updated on 07/Dec/15

$$\mathcal{F}orn=1thereisnosuchdial.$$$$\mathcal{F}orn=2thereis1suchdial.$$$$\mathcal{F}orn=3thereisnosuchdial.$$$$\mathcal{F}orn=4therearetwosuchdials:12341,14321$$$$\mathcal{F}orn=5:$$$$⋮$$$$\mathcal{F}orntherearemsuchdials.\mathcal{W}hatism?$$

Answered by prakash jain last updated on 06/Dec/15

$$\mathrm{No}\mathrm{such}\mathrm{formula}\mathrm{is}\mathrm{possible}\mathrm{due}\mathrm{to}\mathrm{the}\mathrm{fact}\mathrm{that}$$$$\mathrm{there}\mathrm{is}\mathrm{no}\mathrm{formula}\mathrm{for}\mathrm{prime}\mathrm{numbers}.$$

Commented by Rasheed Soomro last updated on 07/Dec/15

$$\mathcal{A}nyimpossibiliyforsometypeofnumbers?For$$$$exampleforoddnumbersetc?$$

Terms of Service
Privacy Policy
Contact: info@tinkutara.com

FacebookTweetPin