Sorry for my reply.
Maybe this trouble based on some of malicious extensions/addons under the browser or other adware under system (if there redirecting from search-results; or if it added certain malicious scripts/advertisements to each visited page).
Do you have installed any security solutions? And if yes - do you have experience with running "Full Scan System" (which can take some hours)? What if such action will detect some malicious activities under system... after this - already there can be another steps.
i use lot of softwares even the issue cannot be solved.
ccleanner , malwarebytes, k7(premium version) etc. ....
even though when open certain websites it dedirect to pron sites and advt...
who to rectify this...?
should router to be replaced?
If you have some devices (like two desktops/laptops or mobile phones/tables) and all of them with this trouble - so most likely something wrong with your network. With such situation you have to re-check router settings (under the web-access - if possible) or contant your ISP-support.
If experience about one device: which OS (like Windows or Mac) or maybe there is mobile device.
Like example - if there Windows system - trouble with redirecting with each browsers? As example - if there modern Windows - can be Internet Explorer, Microsoft Edge or installed browsers like Google Chrome or Firefox.
Google Chrome (as example) provided some tips/tools to cleanup their browser:
If redirecting happened just with certain browser (and not with all of them) - you have to re-check browser's addons/plugins/extensions and shortcut-settings. If there something "suspicious".
if with all browsers - maybe you have to look full system (installed applications; scheduled tasks or other). If there missing something suspicous - I can to think that there required additional steps about scanning system about malware/adware.
For first - it can be some online tools (you noted that already have experience about some software - but strange that nothing found).
For Windows (if there another platform - most likely - possible "related" solutions under certain platform):
--> F-Secure provide Online Scanner: https://www.f-secure.com/en/web/home_global/online-scanner
But if other solutions did not find something - most likely this step also can be with missing result (it more like check for critical places, which should be covered and detected by other popular tools too);
--> Nod32 provide specific scan-tool: https://www.eset.com/us/home/online-scanner/
--> HitmanPro provide scan-tool and you able to use as "trial-time": https://www.hitmanpro.com/en-us/hmp.aspx
Because you noted "malwarebytes" - so probably you also tried their "adwcleaner"-tool;
Some other companies also provided adware-cleaner tools (Bitdefender as example);
If you tried all of them and nothing detected - this is too much strange.
Sorry for my reply.
You also able to contact support of your security solution.
At least -there can be ask - why they do not detected something (even there is certain strange activities under your system).
At least - looks like that there trouble with your Router. Because all devices with such situation.
Basically - you able to re-check things like:
--> open with browser (under device, which connected to your router) IP-address of your router.
--> there can be (or should be) web-panel for administrator-access;
Maybe - if there default credentials (admin/admin as example) - maybe it was exploited.
Or if "router" with kind of "vulnerable"-situation.
Anyway - if you able to login as administrator and re-check settings under the panel:
--> There can be DNS-settings. You able to re-check - if there have strings, which not known for you (or if you not able to get proper results about certain IP from google search);
--> But maybe you able to re-check each available resources/settings about suspicious points.
If situation about this troubles - except step that you have to "reset" (clean/fix and get normal settings for your router) - you also have to think how to prevent such situations else one time.
I not sure about certain steps. At least it should be based on some "backgrounds" and researches.
But maybe you still able to contact ISP Tech Support (if they provided router for you - as example)..
Also you able to re-check web (by Google search as example) about certain model of Router (your router) about some else credentials. Maybe there except "default" (admin/admin or admin/password) - can be some else "manufacturer"-credentials (specific for certain model);
If there missing any options to get support-help from Internet service provider or recover the credentials for router-settings access:
--> maybe your router have buttons "Reset" or something around this "ability". Which should work as "reset" settings and passwords to default (which usually should be visible under the Router-device or instructions to router);
Also just "small" re-check - if you able to use your mobile phone with cellar network access - if there will be missing any troubles with redirecting (when you do not connect by Wi-Fi for your router); This will helpful - if indeed "router"-fix will be enough.
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