X509 Private Key Convert to pkcs1 possible?

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Is it possible to convert a public/private key I created in PHP (x509 format I believe but not 100% sure) to a pkcs1 version (python) ? I have two apps one PHP and one in Python, and I would like them both to use the same key pairs as they will eventually communicate with each other. It doesn't seem to be possible as far as I can tell but could anyone advise if i'm going around in circles with this, or if indeed you can make a key pair work across both programming languages by converting one of them.

My Ultimate aim is:

Python stores - Public key

PHP stores - Private Key

Then both apps perform I/O with each other.

Example of Key made in PHP below (X509)

-----BEGIN PUBLIC KEY----- 
MIIBIjANBgkqhkiG9w0BAQEFAAOCAQ8AMIIBCgKCAQEAqh+pyERnrrSIlJFNcX5D
FI7vJVHlgN0qAVYBsRB7HHGmBXjkFhtbz0RmTE13effnNB5UJS3BzqLFAGib9JkF 
Df7HgnpdVf3pIE5g+2kL/abQ9r+U0qX7hqmwnEWyA60Htz7MpSq4p4q7CPSCeGez 
m7946u8+6jVgIX19YrrM7f4Ai6LBBEFtMG0ytnhVaKWl3kwGuHmCSRUhhZsaE4TZ 
1wce/UcAQSkmzEnflfqdc7IiM55ZPYkW8u9cIFgOhYv3du2Il9GH7E3PBt6aASH/ 
ct7MRP4gCAvoSEhn/t1/Hr/aHlSgH/OIHHK0GFrVUgZokxaYv+EWkfxC9/log5uG 
pQIDAQAB
-----END PUBLIC KEY-----


-----BEGIN PRIVATE KEY----- 
MIIEvQIBADANBgkqhkiG9w0BAQEFAASCBKcwggSjAgEAAoIBAQCqH6nIRGeutIiU 
kU1xfkMUju8lUeWA3SoBVgGxEHsccaYFeOQWG1vPRGZMTXd59+c0HlQlLcHOosUA 
aJv0mQUN/seCel1V/ekgTmD7aQv9ptD2v5TSpfuGqbCcRbIDrQe3PsylKrinirsI 
9IJ4Z7Obv3jq7z7qNWAhfX1iuszt/gCLosEEQW0wbTK2eFVopaXeTAa4eYJJFSGF 
mxoThNnXBx79RwBBKSbMSd+V+p1zsiIznlk9iRby71wgWA6Fi/d27YiX0YfsTc8G 
3poBIf9y3sxE/iAIC+hISGf+3X8ev9oeVKAf84gccrQYWtVSBmiTFpi/4RaR/EL3 
+WiDm4alAgMBAAECggEAYWwEdFUH8vobhMi4ypd9npZDyOFfRi5g0acJDPbdKWrD 
ojqakzZTmxwWYPezxbr7QdNkaG4NoGGB4zwEo0vFo0AVzFh6frYK/J8l1pNPdJBE 
9ii79u1qXrFqG/Olf4lk88EYvDT8zaUaeoRa+syYBEbf3dnn84Nha4xLc3B5zodJ 
A1Ps31utrlHwLYJUHw81jT3aUmKJpV/dqnhb1D8FXd2PN6sNbsA1fDGSBAV5mFll 
u6F5btLwFKpSzCFgT/gbx4LFWR08ZLPpiMWXiUZm5wbBwB0lI8a4qZAXQmHqQokP 
Xj516VAqUdo0eh9sOAZu3h8YNtziOjs/bQoWsek4eQKBgQDfVH5dE7TPc5KjfbaK 
5yBGQDX0ZLMSlXCt35ad79YQlWpMGcvAu5988HiriCntHhOhSeNMNpu/QMmvVL/L 
XZvb9SRSvZzs3kEIP7mxqQi045frq5WxYB4N/nnJmSye4l8oogueTh45y2WrJxsy 
E6Oaiejx0AK5efIUEai0Wrhm5wKBgQDDAqPErtR6Mv/sMtUt76Iun+CfokEN316i 
6s1sDQRTpxCgfDFd7pK77p92LnqGoXpWQoHeRb94d7pCG8UkkvyzfHKyquq4wT2y 
UsDFJ4g+a/x63J43O/NHhW7X5ZShuSRr9+13JWD+P8aqQwIfJd23iST8o5KdDjwF 
c7jkiSYQkwKBgQCbbMhMqqxJPBuvoIvr+5Jgkct6/KILqukyeMrvu7x06ieCMum0 
hl8mqoywhCD5ntb2ht+jaNXXspUqaobYV5ti5yaSVtfhmYQU45Suaf9fNI3EPDP/ 
r+76ukGz5eBB6zVip/QCBkfO3RkylhK9NSHFKXlu4N8kihPJl8ibTA/NvQKBgG+t 
JFIveNjeOfdvCOw8jlk7D6z7g1vJbm3IH4ngTnkFdJ0jYjYTuQ5M0h8g8OQGt4OM 
pMjAkq0Pi6fuNVEDqBm1jA3LmY3ihE2J3IFLaVeuCbHmg+jHuUNdI6QaAqs21qfK 
HMCdtFUF+uRoaV+jFLzVmkvf9MdibncE1X5zGExnAoGAJp7Xe67ZvFrQH7AigXt7 
hxhsvd3/EExTWJx1aGc+aplI1dl8HR6tjBcJSR+uf2siI9B3OuLHaZZha2p/bcE6 
dt2vYbE0/oOunDiU6G3BJFE/gKIVwl4l8sknISLWO/uWg5puig3uK0wbqQawC6G5 
Ude0KAn2vkkHVAgj0oBSqNU=
-----END PRIVATE KEY-----

Thanks

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