According to 1 Tim 6:11 righteousness is something that you should follow.  Paul said, follow after righteousness.

All over the world, righteousness is available to follow.  You find it in the law.  According to the righteousness of the law, Paul was blameless, Phil 3:6.  The law is our school master to bring us to Christ, Gal 3:24.  

Men can also follow after righteousness in their conscience, Rom 2:14-15.  Paul’s conscience was really troubling him.  The Lord said that it was hard for him to kick against the pricks.

Men can follow after righteousness in the gospel, Rom 1:16-17.  Therein the righteousness of God is revealed.  Likewise, the Holy Spirit reproves of righteousness, Jn 16:8.

In the Old Testament observing the law was their righteousness, Deut 6:25.  In the New Testament, Rom 10:4, Christ is the end of the law for righteousness.

In Acts 10:35 Cornelius feared God and worked righteousness.  Therefore, God accepted him, and directed him to Jesus Christ for salvation.  

When you follow after righteousness:

You become righteousness.  See 2 Cor 5:21.  In Gen 15:6 God imputed righteousness to Abraham because he believed God.  God imputes righteousness to a man when he does by faith what God tells him to do.  He tells you to believe on the Lord Jesus Christ.  In Rom 10:9-10 you believe with your heart unto righteousness.  If you haven’t done this yet, you need to believe on Jesus.  And when you do you will be made the righteousness of God in him.

A person who knows the righteousness of God and chooses rather to follow his own righteousness is doing what’s right in his own eyes.  In Judges, this is what the Jews were doing when they had forsaken the righteousness of the law.  And today they won’t submit to the righteousness of God in Jesus Christ, Rom 10:3-4.  When you don’t submit to the righteousness of God in Jesus Christ, you are lost.

You walk in righteousness.   There is a path of righteousness, Ps 23:3.  There is a way of righteousness, Prov 8:20, 12:28, 13:6. Once you have imputed righteousness, you still need to walk in it and be righteous.  We can and must continue in righteousness with the Lord.  It’s not just a matter of not being wicked, it’s a matter of being righteous.  Many Christians stop following after righteousness after they are saved.  Don’t do this.

You serve righteousness.  You can yield to righteousness, Rom 6:18-19, and become the servant of righteousness.  1 Pet 2:24 we should live unto righteousness.  Walking in righteousness leads you to where you are going.  Serving righteousness is how to get there.  When you serve righteousness, you increase in holiness.

Conclusion:  This is why you want to follow after righteousness.  “He loveth him that followeth after righteousness”, Prov 15:9.  “For the righteous Lord loveth righteousness; his countenance doth behold the upright”, Ps 11:7.