Problems & Puzzles: Puzzles

2.- Prime strings 4.- Prime - magical squares 5.- Find Pn =prime >61 such that Pn divides Pn+1*Pn+2 + 1 7.- Palindrome - Primes: 2 questions 8.- Primes by Listing 12.- Period Length of 1/p 13.- Magical Pentagrams 14.- Pal-Primes and sum of powers 15.- Narcissistic pal-primes 19.- Primes on a Clock 21.- Happy Primes 22.- Primes and Persistence 23.- Pal-primes adding consecutive primes 24.- Primes in several bases 25.- Composed primes 26.- Honaker & Jud. McCranie puzzle

27.- Heinz Rectangles 28.- Heinz Stair-case

29.- Pi = P i-1&nxtprm(P i-1), Pi = prime for i => 1 31.- The Average Prime number, APN(k) = S(Pk)/k 34.- Prime Triplets in arithmetic progression 35.- 1999 and the perfect numbers 36.- Sequences of “descriptive primes” 37.- Set of even numbers { ai } such that every ai + aj + 1 is prime 38.- Sloane’s sequences 52.- Sum of K consecutive primes equal to the sum of their reversible ones.

53.- Sequences of consecutive economical numbers.

68.- The largest prime magic squares at the end of this Millennium (a puzzle suggested by Jaime Ayala)

69.- Primeful Heterosquares

70.- Primes Double Tree (a puzzle suggested by Paul Leyland)

71.- Consecutive primes and Cunningham chains

72.- Persistent Palprimes

73.- A Collatz-like sequence.

74.- SOD(26972593-1)

75.- Prime numbers and the number 2000

76.- z(n)=sigma(n) + phi(n) - 2n

77.- Christmas Prime-Pine

78.- Primes by concatenating consecutive integers

79.- The Chebrakov's - by two months - Challenge

80.- Twin primes - magic squares

81.- Sophie Germain  primes - magic squares

82.- The Goldbach Comet

83.- The 6k+1 and 6k-1 boxes

85.- A puzzle about the Generalized Mills' theorem

87.- Adding prime magic squares (a puzzle suggested by John E. Everett)

88.- A special set of odd primes

89.- The first palprime as a sum of consecutive composites

91.- Primes with the Smoothest Increasing Digits (SID primes)

92. A pile of prime-spheres

93.- Numbers such that the decimal and hexadecimal representation are the reverse of each other

94.  The Domino & the primes

95. K consecutive primes p such that the decimal expansion of the reciprocal 1/p, for each p, has exactly a period of length (p-1)

96. The least K consecutive odd primes such that the sum of every two of them produces a distinct number

97. Consecutive numbers with the same "sum of prime factors" (SPF)

100. Digital Prime k-tuplets

101. Digital Divisibility Tests

102. Three squares a cube, all primes

103. N=a4+b4 = c4+d4

104. Numbers that are equal to the sum of cubes of its third parts (as strings)

105. a^5 = b1^5+b2^5+...+bn^5

106. Prime-magic squares added up  to 2000

107. K Consecutive Smith numbers

108. Methods for generating Smith numbers

109. a1<a2<...<ak such that...

110. Dropping digits primes (by Patrick De Geest)

111. Spoof odd Perfect numbers

112. Automorphic primes

113. Provable primes in Arithmetic progression

114. The Murad's generalization of the Collatz's sequences

115. Prime squares composed by no more than two digits

116. A=B+C, A*B*C is a primorial...

117. Certain p# +1 values

118. Primorial product numbers

119. Sophie-Germain & Twin, chains

120. Primal Squares

121. THE  LEGEND  OF  YANG  HUI

122. Consecutive Twin primes

123. Two Frank Rubin's prime puzzles

124. Palindromic, Prime & Sophie-Germain pair of Magic Squares

125. Primes through palindromes

126. Some conspicuous probable primes

130.  The Hexagon of the 19 numbers

131.  Growing primes

132.  Pascal Primes

134.  The 1379-Carrousel-Primes

135.  Partitions into distinct primes with maximum product

136.  Poor prime strings

141.  Smarandache Prime Base representation of the natural numbers

142.  Optimal Assignation of Primes in several Patterns

145.  The ISPP & SSPP functions

146.  Solutions of A2 +X2 = Y2, A = odd

147.  Twin & Reversible primes

148.  Product of primes - 1, a square

149.  Fermat 400

150.  Primes type n+/- Fm, for m=0 to 4

152.  The Prime Gears Cars Race

153.  Espinosa's puzzle

154.  Extension and Variation of the GC

155.  Follow-up of the puzzle 151

156.  One million doors

157.  Zip primes

158.  Sum of Cubes equal to Square of Sum

159.  A follow up to Puzzle 37

161. A Secret Code

176. Primes in a circle

178. Shallit Minimal Primes Set

179. Prime Alphametics

181. (N+k)/k primes

182. Primes with zeros replaced

183. Perhaps a very simple question

184. Gronau's prime triplets

188. Dividing large numbers

192. Reversible & Digit Complementary Prime Pairs

199. The Prime-Vampire numbers

202.  The n-th Omega recurrence

203.  Perfect primes

206.  (N-k)/k primes

207.  The inventory sequences and the self-inventoried numbers

209. Triangles of primes

210. Jeff's numbers

211.  A beauty limit on prime numbers

212.  Substring reversion

213.  Hailstone Champion Sequences

214. Trotter's Curio

215. The Ulam Numbers

216 Primes in a square array

217. n in pn

218. Rupinski primes

220. p - k! primes

221. What are the next?

222. Equations with consecutive primes

223. Consecutive primes and powers of 2

225. VIP (Very Sparse Primes)

229. Primes and Hypercubes

230. Primes and a tower of cubes

231. k-Persistent primes

232. Primes and Cubic polynomials

233. A little twist

234. 2003, again

235. Dropping digits primes

236. A Broken Face

237. Alien neighbors

238. The hidden prime

239. psp (2) & n2 -2 numbers

241.  Highly imperfect primes

242.  Sum of distinct squared primes

244.  Null Conjunction

248.  Find one composite solution

250.  Euler, one more time.

253.  Eureka

254.  Z=P2 - Q2

255.  k*p+1

256.  Jack Brennen old records

259.  Not dividing any pandigital

261.  Symmetric prime constellations

263.  MagicAntiMagic Squares

264.  Antimagic Prime Squares

265.  Primes embedded

266.  Magic rectangles

267.  Talisman Squares

268.  23 primes in A.P.

269.  13 primes in A.P.

270.  Euclidean questions

271.  Prime gap tug of war

273.  Consecutive 'good' primes

274.  Sierpinski triangles from prime numbers

277.  Pi again

278.  The Rupinski's question

279.  Faride Firoozbakht asks for the next term

280.  3893257

281.  A follow up to Puzzle 24

282.  f(p) = f(p')

286.  Get a simple proof of this

288.  Magic squares of (prime) squares

289.  Palprimes inside the infinite primes concatenated

290.  Primes on Platonic solid faces

291.  Primes embedding a given sequence

292.  Zigzag Primes

293.  Balanced primes

294. How to prove this?

295. Another Alphametic puzzle

296. An intriguing sequence

298. Mersene, Mq = (8x)^2 - (3qy)^2

300. UFO message?

301. One million of prime prime residues

305. A new version of Puzzle 209

306. Generalized LYM Puzzle

435. φ(x) + σ(x) = k.x

442. Primes ending in 9

447. Zeros on p.q

454. Number of primes of the form n^2 + 1

462. p+q+r=3*q

466. phi(n-1)=phi(n)=phi(n+1)

471. n and n^2 use only prime digits

473. N = n^p + p^n

474. Two last puzzles for this 2008

475. A question related to ABC Conjecture

478. Factorials as sums of consecutive prime

480. Primes on an Dodecahedron

481. E.E-p=q

494. f(n)=product(prime(di))

497. Sqrt[p^2+q^2- 9]

499. 6*7*8*9 - 1 is prime

502. Adding consecutive 2n+1 primes a prime

508. phi(n)=phi(n+1)

512. b^c=a(mod d)

515. Phi(Phi(x))

517. φ(x) + σ(x+1) = 3x

519. Triangles with prime sides

521. p^p=p mod(q)

522. Three sets of k consecutive primes

523. Increasing residues

524. x = 1 (mod phi(x))

525. D= d1*P1 + d2*P2 +...dn*Pn

526. p2^2-p1^2 = n!

527. sigma(x) = 1 (mod x)

529. The prime-explosion Bergot graph

530. Twins pointing to equidistant trios

531. Two products of consecutive primes a power

532. Puzzle 529 re-loaded: sizing the prime nebulas.

533. phi(sigma(n^2)) = n(n+1)

534. The sum of any two terms a prime or...

535. The minimal seed Xo/Yo for square roots

536. Primes in several bases (again)

537. n^n = n mod [prime(n)]

538. (3n^2+3n+1) ^2 | (3n+1)^(3n+2) + 3n+2

539. n consecutive primes same residue modulo 4

540. b^(2^n)+c

541.- Emirps again

542.- Sigma (x)=q^n

543.- Primes as sum of powered consecutive primes

544.- Yet another  prime Prime Race

545.- 14 or 17<->25

546.- Non-Pandigital primes

547.- A064507

548.- dr(p*n) = dr(n)

549.- Better than 210

550.- Consecutive primes producing semiprimes

551.- Three nines & repunits

553.- SCN=PCP

554. P+10^n

555.- q=p(i) mod [p(i+1)]

557.- H(m, a)

558.- Goldbach decomposition & consecutive primes

560.- Same quantity of prime factors

561.- Square of consecutive prime & even numbers

562.- Heleen's sequence

565.- [(d)n] mod d^n = k

566.- Semiprimes in a given interval

567.- p1+...+pk = q1*...*qk

568.- SOPF(N)=SOPF(RN)

569.- Prime-Magic Hexagon

573.- Primes & its digital roots

574.- P.Q composed by only two distinct digits

575.- Primes | k leftmost digits are divided by p(k)

576.- Triangular Magic Triangles

580. An equivalence for twin primes

581. 142857

583. Traveling intertwined primes

585. 37677869739

588. Squares sharing no one single digit

589. Palindromes multiplying consecutive primes

591. 1304119699

592. p.(p-1)=q&(q+1)

595. p*q -> p^2 + p*q + q^2

596. 12*n*(n+2)+1

600. Follow up to Puzzle 599

607. A zeroless Prime power

609. Rectangling the square.

610. Rectangling the square-II.

611. Puzzle 2-3-5-7.

612. Prime-Doublets.

613. Curio sum of primes.

615. Abs[R(n/3)-n]<=1

616. Primes by dupplicating some digit

617. Concatenating & superposing

618. GCD(1+P, S)

619. Odd midpoints

620. 2012

621. Puzzle 411 revisited

622. Primes as concatenation of two squares

623. p^2+3pq+q^2=r^2

624. Nice integer quotients

625. Sum of squares of prime divisors

626. Frank Rubin, kissing primes

627. Nested Carmichael numbers

628. Fermat Pseudoprimes

629. Non-primitive Carmichael numbers

630. Gap between p(n-1) & p(n+1)

631. Follow up to Puzzle 630

632. [R(n)+1]@n=0

633. Palindromes & Pandigitals

634. Primes in Collatz trajectory

635. 34155

636. Primorial as product of palindromes

637. Factorials as product of palindromes

638. Special integer quotients

639. Sigma (n+12m) = Sigma(n)+12m

640. A sequence of semiprimes.

648. P^2 = A^2&B^2

651 6866683

652 Recursively Pi+1 = POD(Pi) + 1

653 R(p) is n^n.

654 Factors for p(n)#+/-1

655 pq+rs, perfect square.

657 Look and say sequence

659 Sandwiched palindromes

664 The queen covering the chessboard

666 Columns = Rows

667 Puzzle 77

668 Fortyfive

669 2013 and 2014

670 The same sum of divisors

671 Most Perfect Magic Squares

672 sigma(sigma(x)) + sigma(x) = 3x

674 Concatenating the squares of consecutive primes

675 p = -1+2^57885161

676 primes in a row such that...

677 primes in a row such that... II

681 Stanley Antimagic Squares

682 Stanley Antimagic Squares-II

683 Rubin's puzzle

684 Primes in N dice

685 Follow up to puzzle 683

686 Filling the grid (Le Monde puzzle)

687 17769643

688 Follow up to Puzzle 687

689 Pandiagonal and twin primes

690 Unreachable primes

691 Conjectures related to Gilbreath's scheme

692 Consecutive prime gaps biprimes

693 Prime Chemical Compounds

694 S(p,q)=p&q

695 Pandiagonal & twin primes

696 1801

697 Puzzle 105, revisited

698 Others as 129

699 Special prime pandigital magic squares

700 p & q primes such that ...

701 Alphametic magic square

702 Adding emirps to a cube

703 Dividing a set of primes in other two

704 Find a prime such that...

705 2213

707 The smallest sum for a set...

708 Find sets of k consecutive primes such that...

709 Primes P=A&B such that...

710 6252893229398 & non-semiprimes

711 Composites with the exactly the same digits than its prime factors

712 Primes or squares

713 Primes between perfect powers

714 Composites that remain composites when...

715 phi(x + n) = sigma(x - n)

716 Problem 9 of...

717 Associative squares Stanley

718 A follow up to Puzzle 700

719 Extension to Ruth Aaron pairs

720 x^2&y^2 or y^2&x^2 squares

721 p(i)= DR(p(i-1))&(p(i-1)\10)

722 2^m-1 consecutive integers having m prime factors

723. Pandiagonal magic squares of consecutive primes

724. Extending the OEIS sequence A229908

725. The ABA numbers

726. Completing the OEIS sequence A235031

727. Extending the OEIS sequence A235680

729. Consecutive Hoax numbers (extending the OEIS sequence A235766)

730. Trio of Consecutive Achilles numbers

732. Sum of cubes a square

733. Integers equal to the sum of the squares of their prime divisors.

736. Associative Stanley squares of consecutive primes

737. Maximize  log(s) / log(maxPrimeFactor(s))

738. Special Cunningham Chains

739. Carmichael numbers of special form

740. Misprinted product, find the correct one

741. Find the smallest set of distinct primes such that...

742. Prime-Golygons

743. The least largest prime in a 4x4 magic square

744. The smallest prime such that...

745. A number 20 digits large, best qualified

757. Follow-up to Puzzle 756

767. A second Follow up to Puzzle 764.

769. Magic squares and consecutive twin primes.

770. Eygptian Fraction Magic Square

771. First P primes in a square.

773. Necklaces with k primes

798. A nice puzzle by Kamenetski.

799. Follow-up to Puzzle 798.

807. Symmetrical compositions of twin primes

810. Sum of consecutive triangulars and primes

811. Primes and Sum of consecutive triangulars-II

841. Symmetrical compositions of consecutive pairs of cousin primes

868. Magic squares 3x3 and palprimes

872. Integers (p^2)*Q

874.Consecutive integers with increasing or non decreasing quantity of divisors

876.Prime Tuples

877. Integers represented using the minimal first consecutive primes...

878. Consecutive abundant integers

879. More about Q3 from Puzzle 876

880. Consecutive odd abundant integers

881. 123456789 and prime numbers.

882. Prime sequence type A(Z)iB

883. Large three consecutive semiprimes

884. Almost consecutive integers type k-almost primes

885. Square-free almost consecutive integers type k-almost primes

886. The earliest largest set  of consecutive integers type k-almost primes

887. p(n)^c-2 is prime

888. Prime-Squares

889. Prime-Squares-II

890. Magic Squares and Pythagorean Triplets

891. The first N integers arranged to form a Palindrome

893. Primes as a concatenation of a series of powers of 3, with 6m

894. The first N integers X type arranged to form a Palindrome

895. K consecutive quartets of consecutive primes with different ending digit

896. Optimal packing of a set of integers

897. Integers as sum of special Egyptian fractions.

903. Follow-up to Puzzle 902

904. Follow-up to Puzzles 902 & 903

907. 10|p(n)^2 + p(n+1)^2

910. Follow up to Puzzle 908

911. Follow up to Puzzle 910

912. Two successive primes and oblong numbers.

913. The last two digits of a prime is a prime.

914. Puzzle 172, revisited.

915. Follow-up to Puzzles 172 & 914

916. Follow-up to Puzzle 58

917. Q=P+A*B

918. Primes on the line y=x

919. K csc primes without certain ending digit

920. An enigma related to A291582

922. Follow up to Puzzle 634

924. Follow up to Puzzle 923

926. pandigital and prime numbers

940. Digits on p^k

947. Circulant Matrixes and a sequence of primes

1002. Consecutive primes that are also happy numbers

1004. Sum of all the first primes 4k+3 as perfect squares

1005. Palprimes from prime factors of consecutive integers

1006. Bemirps as index of the π(i), the prime counting function.

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