33
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1111 is the only one.
Thre are infinitely many solutions. The smalest set with two different triangular number adding to another is 6 + 15 = 21
2100
To determine the number of prime numbers between 1 and 8888888888888888888888888888888888888888888888, we can use the Prime Number Theorem. This theorem states that the density of prime numbers around a large number n is approximately 1/ln(n). Therefore, the number of prime numbers between 1 and 8888888888888888888888888888888888888888888888 can be estimated by dividing ln(8888888888888888888888888888888888888888888888) by ln(2), which gives approximately 1.33 x 10^27 prime numbers.
If you think about the digits, you can rewrite them as ABBA, with A being one digit and B being another: A can be 1-9 and B can be 0-9. Since A has to be 1, B can be 0-9, leaving 10 palindromic numbers.