Problems & Puzzles:
Puzzles
1.- The Gordon Lee puzzle
2.- Prime strings 
3.- Magic Squares with
consecutive primes
4.- Prime - magical squares
5.- Find Pn =prime >61 such
that Pn divides Pn+1*Pn+2 + 1
6.- Ray Ballinger suggestion
7.- Palindrome - Primes: 2
questions
8.- Primes by Listing
9.- p1 + p2 + … pk = n m ,
m => 2
10.- Primes associated to
Primorials and Factorials
11.- Distinct, Increasing &
Decreasing Gaps
12.- Period Length of 1/p
13.- Magical Pentagrams
14.- Pal-Primes and sum of
powers
15.- Narcissistic pal-primes
16.- Consecutive primes and
ending-digit
17.- Weakly primes
18.- Some Special Sums of
Consecutive Primes
19.- Primes on a Clock
20.- Reversible Primes
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
30.- Queen attacking primes in
a Knight’s tour solution
31.- The Average Prime
number, APN(k) = S(Pk)/k
32.- Find couples of numbers
like this (1033, 8) such that:
1033 = 8^1+8^0+8^3+8^3
33.- Find numbers like
this:15551(palprime)= Fifteen Thousand Five Hundred Fifty
One = 383 (palprime)
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
39.- The Mirrorable Numbers (By
Mike Keith)
40. The Pi Prime Search Puzzle
(by Patrick De Geest)
41. Palindromic Carnival
(dedicated to Patrick De Geest)
42.- This week puzzle is to
create a puzzle analog to other one.
43.-Palprime1*Palprime2 =
Palindrome
44.-Enoch Haga Puzzle about
Consecutive Primes
45.- Prime Solitaire (a puzzle
based on a game proposed by Enoch Haga)
46.- Primes expressible as
sum of consecutive primes in K ways
47.- p4 = a4 +
b4 + c4 + d4, {a, b, c,
d}>0
48.- P3 = a3
+ b3 + c3, {P, a, b, c} = primes
49.- “If you are given
K numbers of each from 0 to 9, find the maximum quantity
of primes that can be formed using those 10K
numbers”.
50.- “The best approximation to Pi with primes”
51.- Pi such that Pi is Palprime & i = palindrome
52.- Sum
of K consecutive primes equal to the sum of their reversible ones.
53.- Sequences of consecutive
economical numbers.
54.- Pair of primes of the
form {p, 4p^2+1}
55.- Primes by Generation (Patrick De
Geest)
56.- The
Honaker's Constant
57.- 8757193191, another little puzzle from Mike Keith
58.- A
particular sequence of k consecutive primes (by Enoch Haga)
59.- Six and the nine digits primes (by Jud
McCranie)
60.- Generalized
Cunningham chain (By Felice Russo)
61.- M(a,
p) = a^p - a + 1 ( by Jean
Brette)
62.- The qs-sequence, (by T.W.A. Baumann)
63.- Another (3rd) Mike Keith's little
puzzle.
64.- The Strange Ruler (TWA Baumann)
65.- Multigrade Relations
66.- The SOPF sequences
67.- The
P/M-SOPF sequences
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
84.- Non-primes
adding up to non-primes (by TWA)
85.- A puzzle
about the Generalized Mills' theorem
86.- Disjoint sets
A & B of consecutive numbers sharing the same set P of prime divisors
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
90.- The prime version of the
taxicab
problem
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)
98. Curio 39
99. Primes p such
that R(p) is prime and p^2 = R(R(p)^2)
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
127. Non
adding prime sequences
128. Sum of
consecutive squared primes a square
129. Harshad
Numbers
130. The
Hexagon of the 19 numbers
131. Growing
primes
132. Pascal
Primes
133. Pa
- Qb = K
134. The
1379-Carrousel-Primes
135. Partitions
into distinct primes with maximum product
136. Poor
prime strings
137. Product
of primes + 1, a square
138. Deletable
primes
139. Sdf(x)=p
140. Primes
Decades
141. Smarandache
Prime Base representation of the natural numbers
142. Optimal
Assignation of Primes in several Patterns
143. The first and the
last five primes
144. The
Langford Prime Numbers
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
151.
Euler-Rodríguez set of consecutive primes
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
160.
s(n)
and p(n)
161. A
Secret Code
162. P2
+ Q2 = p2 +q2
163. P+SOD(P)
164. Sequences of Fermatian primes
165.
Bye Mr. Suzuki
166. pn -1 =0 mod
f(n)
167.
Primes m + 2 j &
m - 2 j
168.
Primes such that SOD2 = POD
169. The unit and the sum of
three signed prime-cubes
170. Pseudoprimemania
171. Perfect &
Carmichael numbers
172. Minimal Length,
prime-complete-rules
173. Ruth-Aaron Triplets
174. Primes & consecutive
divisors
175. Integer average & sets of
consecutive primes
176. Primes in a circle
177. Primes in a
square
178. Shallit Minimal Primes
Set
179. Prime
Alphametics
180. Primes as a sum of squares
181. (N+k)/k
primes
182. Primes with zeros
replaced
183. Perhaps a very simple question
184. Gronau's
prime triplets
185. Differences
between consecutive n^n values
186. Squareful Fibonacci numbers
187. Triangles and Triangular numbers
188. Dividing large numbers
189. Squares and primes in a row
190. A follow up for the puzzle 188
191. P(n)=n(n+1)(n+2)(n+3) - 1
192. Reversible
& Digit Complementary Prime Pairs
193. The Andersen's theorem & primes
194. The Palinpoints
195. Primes such that their squares are
free of the digit D.
196. Consecutive integers with the same quantity of prime
factors
197. Always
composite numbers?
198. 2^a - 3^b = c
199. The
Prime-Vampire numbers
200. Ones from
1 to p (*)
201. The arithmetic function A(n)
202. The n-th Omega
recurrence
203. Perfect primes
204. An old
empirical observation
205. Primes is in CI
206. (N-k)/k primes
207. The inventory
sequences and the self-inventoried numbers
208. Happy new Year 2003!
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
219. Polignac numbers
220. p - k! primes
221. What are the next?
222. Equations with consecutive primes
223. Consecutive primes and powers of 2
224 Eccentric prime diagonals
225. VIP (Very
Sparse Primes)
226. Rolling Primes
227. Research Problem 1.75
228. Sum of twin primes, a square
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
240. Consecutive
numbers and consecutive prime factors
241. Highly
imperfect primes
242. Sum of distinct squared
primes
243. Primes and squares in a
square array
244. Null Conjunction
245. As 13
246. The worms
247. Consecutive Smith
numbers
248. Find one composite solution
249. From
Rudolf to Rodolfo (magic squares and pandigital numbers)
250. Euler, one more time.
251.
Pointer primes
252.
Kurchan
squares
253. Eureka
254. Z=P2 - Q2
255. k*p+1
256. Jack Brennen old
records
257. Primes and sibling
numbers
258. Primes
and sibling numbers-II
259. Not dividing any
pandigital
260. Chains of twins
261. Symmetric prime
constellations
262. Semiprimes in
arithmetic progression
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
272. P(n) & n
273. Consecutive 'good'
primes
274. Sierpinski triangles from prime
numbers
275. Highly composite polynomials
276. Prime factors of
(x^n+y^n)/(x+y)
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')
283. Harshad Left
Truncatable numbers
284 A+B=C | A.B.C = pk#
285. μ(2^k-1) mod k
286. Get a simple proof of
this
287. Multimagic prime squares
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
297. Queens
on magic squares
298. Mersene, Mq = (8x)^2 - (3qy)^2
299. Collatz-like sequence of
primes
300. UFO message?
301. One million of prime prime
residues
302. Primes inside the
sequence of primes
303. I'm such a square...
304. A larger square embedded
305. A new version of Puzzle 209
306. Generalized LYM Puzzle
307. Record
Smith Numbers
308. AxB = N =A'xB'
309. A property of the prime '5'
310. DPT's on a knight's tour.
311. Sum to a cube
312. Sequence of primes such that...
313. Squares having only k distinct digits
314.
(f(n))=prime(n)
315. pn => pn-i + pi
316. Divide a square of primes.
317. Two dimensional constellation of primes
318. 31 = sigma(16) = sigma(25)
319. Approximations to π(n)
320. Dealing with primorials
321. Primes type n^4+4
322. Primeval primes as sum of primeval primes
323. Primes in a Sudoku
solution
324. Self-descriptive numbers
325. Zeisel numbers
326. One more Firoozbakht curio sequence
327. Giuga numbers
328. Is this the largest?
329. Odd abundant numbers not divided by 2 or 3.
330. σ(φ(σ(p)))=φ(σ(φ(p)))
331. The prime Russian mountain
332. Odd abundance
333. 'Magic squares' and primes
334. Faride & the 2004 year.
335. Prime values for σ(n).
336. sigma(n)<prime(n)
337. p inside p2.
338. Domino-Prime-Pyramid
339. Primes & persistence.
340. Resta's approach to Puzzle 337
341. Multiplicative persistence, Erdos style.
342. Primes on a dice.
343. One more Faride's question
344. Primes in Nature
345. Magic square of cubic primes
346. Happy 2006
347. Properties of numbers
that have a Mersenne Number as a factor
348. 414347 prime string
349.
2d(n) = n + E
350. Primes &
primorials
351. E796
352.
φ(n!)
353. The first
n2 primes in a matrix
354. Another
prime game
355. Puzzle 232
in 4th order
356. A minimal
set of K primes
357. Consecutive
reversible primes
358.
Ruth-Aaron pairs revisited
359. First N
primes in a circle
360.
Complementary divisors to make a prime
361.
Multiply, or delete zeros
362. A sequence
of primes.
363. A
magnanimous company
364. P2 = Q*R
365. P*Q = R*S
366.
Three questions about the PGP
367.
Two dice to produce prime numbers
368.
Attained by invalid arithmetic
369.
Approximations to unit adding prime reciprocals.
370. The first
13 numbers
371. A052215
372. Ask Dr.
Matrix, prime version
373. Self primes
374. Self
numbers
375. Powers
which are the sum of initial primes
376.
n=p*2^x
377.
Add 2 to any digit
378. Sequences
embedded in decimal periods of fractions
379. SG primes
and its prime average
380. A follow up
to Puzzle 42
381. A
sequence related to a special case of the Goldbach Conjecture
382.
KL(29207), Prime or Composite?
383. Brougnard
sequences
384. Prime
Reverse Keith numbers
385
Follow up to Puzzle 104
386. CabTaxi,
prime version
387. Prime
curios in the Pascal's triangle rows?
388. Primes on a dice, again
389. Joe Crump
and the search for solutions to 2nmod n=c
390. 493009335
391. 9 dots, 8
lines
392. σ(x) =
x+φ(x)
393. A follow up
to Puzzle 128
394. No shared digits between composites and its
prime factors
395.
(2^n+3^n+4^n+5^n+6^n)/2 – 10
396. X*R=Y
397. 15984784979
398. 369293
399. Some more
terms
400. 39883
401. Magnanimous
primes
402. 1263560563
403. 833021343
404.
Σ(x^x), for x=1 to n
405. R(38)
406. 1123
407. Prime Multidimensional Arithmetic Progressions
408. First
primes embedded in the smallest number
409. Consecutive
primes triplets
410. The largest magic
square & primes...
411. Magic
squares M & p(M)
412. Semimagic square of cubes
413. DPS in AP
414. Prime lucky number
triplets
415. Sets of
consecutive primes such that...
416.
Prime numbers less than 2^18
417. M(e)
reversed primes.
418.
Honaker's ratio
419.
Four SOPF questions
420. Another
sequence of primes
421.
Staircase of consecutive primes
422. 3N
consecutive prime
423. K Consecutive
even numbers such that...
424. Empty
intervals between consecutive perfect powers
425.
Consecutive numbers, increasing quantity of prime factors
426. q = p
+rad(p+1)
427. Runs of
consecutive numbers such that... (I)
428. Runs of
consecutive numbers such that... (II)
429.
Consecutive primes & biprimes
430.
Grimm's conjecture
431. p = (q/r)3 + (s/t)3
432. A
nice pattern with 6 consecutive primes
433. Three consecutive integers
434.
σ(σ(x)) = σ(x)+x
435.
φ(x) + σ(x) = k.x
436. 43 =4^2+3^3
437. A special set of binary numbers
438. 1024383257
439.
Fibonacci Primes Puzzle
440.
σ(n)=2n-1
441.
σ(n)+π(n)=k.n
442. Primes ending in 9
443.
Sum of cubes of consecutive primes
444.
Pseudo twin primes
445.
Consecutive integers with prime SPF
446.
S(p, q)=p.q
447. Zeros on p.q
448. p+q not divided by 3
449. Count N composites after p
450.
K extended factors for sum of two consecutive primes
451. Prime factors of n,
φ(n) & σ(n)
452.
(a^2)!+2^(a^2) = b*(1+a^2)
453.
DPFP 
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