The 'primary name server not listed at parent' error in MXToolbox, when using Squarespace, generally arises from a mismatch between the nameservers configured at your domain registrar (Squarespace) and those defined in the DNS zone file. The solutions revolve around verifying and correcting these records, ensuring consistency and accuracy. DNS propagation delays of up to 48 hours are common and can temporarily cause this error. Glue records are critical if your nameservers are subdomains of your main domain, requiring careful attention. Further, double-checking the SOA record, using DNS lookup tools, and ensuring A records point to the correct location can aid in identifying and resolving discrepancies. If troubleshooting doesn't work, contacting Squarespace support is recommended.