If you have numerical evidence in support of the conjecture, the journal of Experimental Mathematics seems to fit the bill:

Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses.

Note that we do value proofs: experimentally inspired results that can be proved are more desirable than conjectural ones. However, we do publish significant conjectures or explorations in the hope of inspiring other, perhaps better-equipped researchers to carry on the investigation. The objective of Experimental Mathematics is to play a role in the discovery of formal proofs, not to displace them.

If you have numerical evidence in support of the conjecture, the journal of Experimental Mathematics seems to fit the bill:

Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses.

Note that we do value proofs: experimentally inspired results that can be proved are more desirable than conjectural ones. However, we do publish significant conjectures or explorations in the hope of inspiring other, perhaps better-equipped researchers to carry on the investigation. The objective of Experimental Mathematics is to play a role in the discovery of formal proofs, not to displace them.

Several publications in that journal have gotten quite some traction, like:

• Mahler's Measure and Special Values of L-functions

• New Conjectural Lower Bounds on the Optimal Density of Sphere Packings

• Kashaev’s Conjecture and the Chern-Simons Invariants of Knots and Links

• About a new kind of Ramanujan-type series

The journal of Experimental Mathematics seems to fit the bill:

Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses.

Note that we do value proofs: experimentally inspired results that can be proved are more desirable than conjectural ones. However, we do publish significant conjectures or explorations in the hope of inspiring other, perhaps better-equipped researchers to carry on the investigation. The objective of Experimental Mathematics is to play a role in the discovery of formal proofs, not to displace them.

If you have numerical evidence in support of the conjecture, the journal of Experimental Mathematics seems to fit the bill:

Experimental Mathematics publishes original papers featuring formal results inspired by experimentation, conjectures suggested by experiments, and data supporting significant hypotheses.

Note that we do value proofs: experimentally inspired results that can be proved are more desirable than conjectural ones. However, we do publish significant conjectures or explorations in the hope of inspiring other, perhaps better-equipped researchers to carry on the investigation. The objective of Experimental Mathematics is to play a role in the discovery of formal proofs, not to displace them.