Problems & Puzzles: Puzzles

 Puzzle 1070 Happy Holidays puzzle with atomic numbers For sure you know that each one of the chemical elements is numerically characterized by an integer named "atomic number". This integer number is equal to the  quantity of protons inside the nucleus of the chemical element. BTW, the greater atomic number of all the currently known chemical elements is 118, corresponding to the Organesson. And ALL the chemical elements from atomic number from 1 to 118 has been discovered in our planet nowadays. A very simplified Periodic Table of all the known chemical elements can be described by a set of 118 cards having three basic data: 1) the Name of the Chemical element, 2) Its Symbol or abbreviation and 3) Its Atomic number. By example, in the figure above The first card correspond to the chemical element named "Hierro" (in Spanish), whose abbreviation is "Fe" and whose atomic number is 26. Q1. Can you provide other examples of interesting names or phrases made with the cards corresponding to the chemical elements? Example: "Pure Fun"-> Pluronium.Rhenium.Fluor. Uranium. Nitrogen -> 94.75.9.92.7 Q2. What is the largest prime number you can form concatenating all the possible atomic numbers just once? Q3. Redo Q2 for an emirp Q4. Redo Q2 for a palprime. Note: Please send your solutions separating each atomic number by a dot.

During the week 1-7 Jan, 2022, contributions came from Claudio Meller, Giorgos Kalogeropoulos, Oscar Volpatti, Emmanuel Vantieghem.

***

Claudio wrote:

Hola, el mayor primo que encontré es :
999989796959493929190898888786858483828180797877776757473727170696867666656463626160595857565555
453525150494847464544443424140393837363534333323130292827262524232222120191817161514131211811711
611511411311211111111010910810710610510410102100103101

(99, 9, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 8, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 7, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 6, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 5, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 4, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 3, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 2, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 118, 117, 116, 115, 114, 113, 112, 111, 11, 1, 110, 109, 108, 107, 106, 105, 104, 10, 102, 100, 103, 101)

El mayor emirp:

99998979695949392919089888878685848382818079787777675
747372717069686766665646362616059585756555545352515049
484746454444342414039383736353433332313029282726252423
22221201918171615141312118117116115114113112111111110
10910810610010310210510410101107
(99, 9, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 8, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 7, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 6, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 5, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 4, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 3, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 2, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 118, 117, 116, 115, 114, 113, 112, 111, 11, 1, 110, 109, 108, 106, 100, 103, 102, 105, 104, 10, 101, 107)

Frases interesantes:

Re-s-o-lv-er co-n pr-i-mo-s

La palabra más larga que se puede escribir con los símbolos en inglés según varias páginas es :

No-n-Re-p re se-n- ta-ti-o-na-li-sm-s

Mi país:  Ar-ge-n-ti-na

En este sitio, http://www.nandor.org/math/chemwords/chemwords.htm
hay un listado con todas las palabras en inglés que pueden escribirse con los símbolos químicos, así como también países y nombres.

y en este sitio : https://www.chemspeller.com/index.html? , puedes probar si una palabra se puede escribir con los símbolos de los elementos químicos

***

Giorgos wrote:

Q1: "Genius Recreations Infuse Lunar Brains"  ->  Germanium, Nickel, Uranium, Sulfur, Rhenium, Carbon, Rhenium, Astatine, Iodine, Oxygen, Nitrogen, Sulfur, Indium, Fluorine, Uranium, Selenium, Lutetium, Sodium, Rubidium, Radium, Indium, Sulfur -> 32, 28, 92, 16, 75, 6, 75, 85, 53, 8, 7, 16, 49, 9, 92, 34, 71, 11, 37, 88, 49, 16

Q2: 99. 9. 98. 97. 96. 95. 94. 93. 92. 91. 90. 89. 88. 8. 87. 86. 85. 84. 83. 82. 81. 80. 79. 78. 77. 7. 76. 75. 74. 73. 72. 71.
70. 69. 68. 67. 66. 6. 65. 64. 63. 62. 61. 60. 59. 58. 57. 56. 55. 5. 54. 53. 52. 51. 50. 49. 48. 47. 46. 45. 44. 4. 43. 42. 41.
40. 39. 38. 37. 36. 35. 34. 33. 3. 32. 31. 30. 29. 28. 27. 26. 25. 24. 23. 22. 2. 21. 20. 19. 18. 17. 16. 15. 14. 13. 12. 118.
117. 116. 115. 114. 113. 112. 111. 11. 110. 109. 108. 107. 106. 105. 104. 1. 100. 102. 103. 10. 101

Q3: 99. 9. 98. 97. 96. 95. 94. 93. 92. 91. 90. 89. 88. 8. 87. 86. 85. 84. 83. 82. 81. 80. 79. 78. 77. 7. 76. 75. 74. 73. 72. 71.
70. 69. 68. 67. 66. 6. 65. 64. 63. 62. 61. 60. 59. 58. 57. 56. 55. 5. 54. 53. 52. 51. 50. 49. 48. 47. 46. 45. 44. 4. 43. 42. 41.
40. 39. 38. 37. 36. 35. 34. 33. 3. 32. 31. 30. 29. 28. 27. 26. 25. 24. 23. 22. 2. 21. 20. 19. 18. 17. 16. 15. 14. 13. 12. 118.
117. 116. 115. 114. 113. 112. 111. 11. 1. 110. 109. 108. 106. 100. 103. 102. 105. 104. 10. 101. 107

***

Oscar wrote:

Yesterday my family celebrated the Epiphany of Jesus, along with the fifth birthday of my daughter Carola, so:
6.18.8.57.16.5.77.90 = CArOLa'S BIrTh.

About numbers obtained by concatenating atomic integers from 1 to n = 118. We have some degrees of freedom when similar repdigits (like 1,11, and 111) are in consecutive positions.
I sorted them by decreasing length.

Largest number (composite):
99.9.98.97.96.95.94.93.92.91.90.89.88.8.87.86.85.84.83.82.81.80.79.78.77.7.76.75.74.73.72.71.70.69.68.67.66.6.65.64.63.
62.61.60.59.58.57.56.55.5.54.53.52.51.50.49.48.47.46.45.44.4.43.42.41.40.39.38.37.36.35.34.33.3.32.31.30.29.28.27.26.
25.24.23.22.2.21.20.19.18.17.16.15.14.13.12.118.117.116.115.114.113.112.111.11.1.110.109.108.107.106.105.104.103.
102.101.10.100

Largest prime (permutation of last five atomic integers):
99.9.98.97.96.95.94.93.92.91.90.89.88.8.87.86.85.84.83.82.81.80.79.78.77.7.76.75.74.73.72.71.70.69.68.67.66.6.65.64.63.
62.61.60.59.58.57.56.55.5.54.53.52.51.50.49.48.47.46.45.44.4.43.42.41.40.39.38.37.36.35.34.33.3.32.31.30.29.28.27.26.25.
24.23.22.2.21.20.19.18.17.16.15.14.13.12.118.117.116.115.114.113.112.111.11.1.110.109.108.107.106.105.104.10.102.100.
103.101

Largest emirp (permutation of last nine atomic integers):
99.9.98.97.96.95.94.93.92.91.90.89.88.8.87.86.85.84.83.82.81.80.79.78.77.7.76.75.74.73.72.71.70.69.68.67.66.6.65.64.63.
62.61.60.59.58.57.56.55.5.54.53.52.51.50.49.48.47.46.45.44.4.43.42.41.40.39.38.37.36.35.34.33.3.32.31.30.29.28.27.26.25.
24.23.22.2.21.20.19.18.17.16.15.14.13.12.118.117.116.115.114.113.112.111.11.1.110.109.108.106.100.103.102.105.104.10.
101.107

No palprime.
Any concatenation has length 246, with:
digit 1 used 50 times;
digits 2 to 8 used 22 times;
digits 0 and 9 used 21 times;
so we can generate no palindrome at all.
In order to have a palprime we need:
odd length (otherwise divisibilty by 11);
exactly one digit with odd frequency;
digit sum not divisible by 3.
So we can't find palprimes unless n = 19,22,40,61,79,121,...
Or maybe we can search for a 245-digit palprime after dropping Fluorine (Z=9).

***

Emmanuel wrote:

Q2 :
This is my biggest prime number :
99.9.98.97.96.95.94.93.92.91.90.89.8.88.87.86.85.84.83.82.81.80.79.78.77.7.76.75.74.73.72.71.70.69.68.67.66.
6.65.64.63.62.61.60.59.58.57.56.55.5.54.53.52.51.50.49.48.47.46.45.44.4.43.42.41.40.39.38.37.36.35.34.33.3.32.
31.30.29.28.27.26.25.24.23.22.2.21.20.19.18.17.16.15.14.13.12.118.117.116.115.114.113.112.111.11.110.109.
108.107.106.1.10.101.104.105.100.102.103 (246 digits).

Q3 :
This is my biggest emirp :
99.9.98.97.96.95.94.93.92.91.90.89.8.88.87.86.85.84.83.82.81.80.79.78.77.7.76.75.74.73.72.71.70.69.68.67.66.
6.65.64.63.62.61.60.59.58.57.56.55.5.54.53.52.51.50.49.48.47.46.45.44.4.43.42.41.40.39.38.37.36.35.34.33.3.32.
31.30.29.28.27.26.25.24.23.22.2.21.20.19.18.17.16.15.14.13.12.118.117.116.115.114.113.112.111.11.110.109.
108.1.105.104.10.100.102.106.101.103.107 (246 digits).

Q4.
It is impossible to find all atomic numbers just once in a palprime.
This is because the set of all atomic numbers uses  246  digits :
digit 1 is used 51 times;
digits 2, 3, 4, 5, 7, 8  and  9  are used 22 times;
Digit 6 is used 23 times;
digit 8 is used  21  times.
No palindrome has such a configuration : all digits should occur an even number of times.

If we do not need to use all atomic numbers, then my biggest palprime is
99.8.97.96.95.94.93.92.91.87.86.85.84.83.82.81.76.75.74.73.72.71.70.1.65.64.63.62.61.54.53.52.51.32.31.
43.42.41.21.60.11.106.12.14.24.34.13.23.15.25.35.45.16.26.36.46.56.10.7.17.27.37.47.57.67.18.28.38.48.
58.68.78.19.29.39.49.59.69.79.89.9
Unused atomic numbers :
2, 3, 4, 5, 6, 20, 22, 30, 33, 40, 44, 50, 55, 66, 77, 80, 88, 90, 98, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118
I'm almost sure there must be bigger solutions.

***

On Feb 25, 2022, Claudio Meller wrote:

Q4.

Te mando el palprime que encontré para este puzzle:

Largo total=  193
99897969594939291868587848382817767475737271656364626155452535143414
23322131118806670322010410511150140102230766088111312233241434153525
455162646365617273757476771828384878586819293949596979899

Números usados : 9, 98, 97, 96, 95, 94, 93, 92, 91, 86, 85, 87, 84, 83, 82, 81, 77, 6, 74, 75, 73, 72, 71, 65, 63, 64, 62, 61,
55, 4, 52, 53, 51, 43, 41, 42, 33, 2, 21, 31, 118, 80, 66, 70, 32, 20, 104, 105, 111, 50, 1, 40, 10, 22, 30, 76, 60, 88, 11, 13, 12,
23, 3, 24, 14, 34, 15, 35, 25, 45, 5, 16, 26, 46, 36, 56, 17, 27, 37, 57, 47, 67, 7, 18, 28, 38, 48, 78, 58, 68, 19, 29, 39, 49, 59, 69, 79, 8, 99.

Números no usados : 116, 110, 100, 115, 89, 109, 114, 112, 106, 44, 101, 108, 107, 103, 102, 90, 117, 54, 113.

A few hours later himself wrote:

Encontré otro mayor:

Largo total=  197

99897969594939291868587848382817767475737271656364626155452535
14341423322110831110445076602230109101901032206670544011138011
22332414341535254551626463656172737574767718283848785868192939
49596979899

Números usados : 9, 98, 97, 96, 95, 94, 93, 92, 91, 86, 85, 87, 84, 83, 82, 81, 77, 6, 74, 75, 73, 72, 71, 65, 63, 64, 62, 61, 55,
4, 52, 53, 51, 43, 41, 42, 33, 2, 21, 108, 31, 110, 44, 50, 76, 60, 22, 30, 109, 101, 90, 10, 32, 20, 66, 70, 54, 40, 11, 13, 80, 1, 12, 23, 3, 24, 14, 34, 15, 35, 25, 45, 5, 16, 26, 46, 36, 56, 17, 27, 37, 57, 47, 67, 7, 18, 28, 38, 48, 78, 58, 68, 19, 29, 39, 49, 59, 69, 79, 8, 99.

Números no usados : 88, 111, 103, 114, 113, 106, 117, 105, 104, 102, 116, 107, 118, 89, 100, 112, 115.

Sigo buscando

***

Claudio Meller wrote on March 2022:

Y este el que encontré mayor:

Largo total=  197

998979695949392918685878483828177674757372716563646261554525351434142332211188032205440766011310
911190131106670445022308811122332414341535254551626463656172737574767718283848785868192939495969
79899

Números usados : 9, 98, 97, 96, 95, 94, 93, 92, 91, 86, 85, 87, 84, 83, 82, 81, 77, 6, 74, 75, 73, 72, 71, 65, 63, 64, 62, 61, 55, 4, 52, 53, 51, 43, 41, 42, 33, 2, 21, 118, 80, 32, 20, 54, 40, 76, 60, 113, 109, 111, 90, 13, 1, 10, 66, 70, 44, 50, 22, 30, 88, 11, 12, 23, 3, 24, 14, 34, 15, 35, 25, 45, 5, 16, 26, 46, 36, 56, 17, 27, 37, 57, 47, 67, 7, 18, 28, 38, 48, 78, 58, 68, 19, 29, 39, 49, 59, 69, 79, 8, 99.

Números no usados: 103, 102, 106, 107, 101, 116, 110, 100, 115, 117, 108, 114, 31, 104, 89, 112, 105.

***

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