mjhjmtu

right now I have an assignment that I have to build a software which can encrypt/decrypt by RSA method. I already did it, but my teacher said that I need to find a test suite (include: modulus, public key, private key) to test if my software runs correctly and he doesn't accept any random data (although that data is correct). He needs real data which already tested by someone else and that data need to be mentioned in lectures, books, reports, benchmarks,... I tried to find them but I cannot :(. I'm very appreciated if you can help me.
Thank you.

There are RSA keys pairs in the validation suite for the RSA part of FIPS 186-4 (see second part of this answer for details).

Because "encrypt/decrypt by RSA method" is not well-defined (for lack of indication of the padding method), there's no way to tell which Known Answer Test vectors for it fit the question's need.

Also, only the decryption code can be tested with fixed KAT: RSA encryption with proper random padding is not deterministic, thus its code needs to be modified (de-randomized) for testing against KAT.

FIPS 186-4 is a standard for digital signatures per a variety of methods, including several RSA-based. It has a test suite, with at the bottom of the page links to files with test vectors. The one for FIPS 186-4 RSA-based functions is 186-3rsatestvectors.zip. It contains several keys pairs. For example, SigGenPSS_186-3.txt starts with

[mod = 2048]

n = 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

e = 0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000086c94f
d = 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

Note: $mathttmod$ is the bit size of the public modulus, expressed in decimal. $mathtt n$, $mathtt e$ and $mathtt d$ are the public modulus, the public exponent, and the FIPS 186-4-mandated private exponent, expressed in hexadecimal. Therefore, $mathtt d$ was obtained as $mathtt e^-1bmodlambda(mathtt n)$ (where $lambda$ is Carmichael's function), but is usable just as $mathtt e^-1bmodvarphi(mathtt n)$ would be (where $varphi$ is Euler's totient), another common private exponent in RSA.

For the modulus $n=pq$ you need to verify that $p$ and $q$ are prime numbers. You can do this with a probabilistic primality test like Rabin-Miller.
For the public key $e$ you need to verify that it is coprime to the euler totient $phi (n)$ you can do this with the extended Euclidean algorithm.
For the private key $d$ you need to verify that $de equiv 1 pmod n$. You can do this with the extended Euclidean algorithm.