Tuesday, December 10, 2019

1972 and Paul numbers

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1972 е единственото число, с идентични цифри в числото и множителите, които са прости числа. 1972 = 2 × 2 × 17 × 29.
ПЧ#294 = 1973. 
1972 = 6^2 + 44^2 = 26^2 + 36^2.

12+17+19+21+27+29+71+72+79+91+92+97 = 627 = 33 × 19

127 = PR#27, 172 = 4 × 43, 217 = 7 × 031, 
271 = PR#56, 712 = 8 × 89, 721 = 7 × 103.
129 = 3 × 43, 192 = 16 × 04 × 3, 219 = 3 × 073,
291 = 3 × 97, 912 = 16 × 19 × 3, 921 = 3 × 307.
179 = PR # 37, 197 = PR # 41, 719 = PR#124,
791 = 113 × 7, 917 = 7 × 131, 971 = PR#160.
279 = 3 × 3 × 031, 297 = 3 × 3 × 3 × 11, 729 = 3 × 3 × 3 × 3 × 3 × 3
927 = 3 × 3 × 103, 792 = 8 × 3 × 3 × 11, 972 = 4 × 3 × 3 × 3 × 3 × 3

1279 = PR#203
1297 = PR#207
1729 = 7 × 13 × 19
1792 = 256 × 7
1927 = 41 × 47
1972 = 4 × 17 × 29
2179 = PR#323
2197 = 13 × 13 × 13
2719 = PR#393 = 3*131
2791 = PR#402 = 67*6
2917 = PR#418 = 2*11*19
2971 = PR#425 = 25*17
7129 = PR#910 = 2 * 5 * 7 * 13
7192 = 8 × 29 × 31
7219 = PR#919 (919=PR#153)
7291 = 23 × 317=PR#62
7912 = 8 × 23 × 43 (PR#5+10)
7921 = 89 × 89=PR#20
9127 = PR#1127
9172 = 4 × 2293=PR#336
9217 = 13 × 709=PR#2+123
9271 = 73 × 127=PR#17+27
9712 = 16 × 607=PR#107
9721 = PR#1195
126654 = 606 × 19 × 11
12654 = 6 × 19 × 111
627 = 3 × 19 × 11
126654 +12654 + 627 = 139935 = 3 × 5 × 19 × 491

11 - Primes, 1+2+7+9 = 19, 1*9*7*2 = 126 , 21 + 79 = 100
1972 = 4 × 17 × 29
1975 = 5 ×   5 × 79, 1975,5 = 45 × 439.
1976 = 8 × 13 × 19, 1975,6 = 44 × 449.

1972 = 4*17*29
1) 1*9*7*2 = 126 (126 - 50 = 76)
2) 4+17+29 = 50 (26 + 50 = 76)
3) (2179 = PR#323) 3*23 = 69 > 3,5 (50 + 19 = 69)
4) 04 (1792 = 4^4 × 7) Надолу са множителите
5) 07 (1927 = 41 × 47)
6) 47 (2917 = PR#417)
7) 68 = 4*17, (4 + 7 + 47 + 68 = 126)
8) 76 = 4*19, (9721 = PR#1195)

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