diff --git a/runtime/src/bank.rs b/runtime/src/bank.rs
index 5567211296..bdd223f2cf 100644
--- a/runtime/src/bank.rs
+++ b/runtime/src/bank.rs
@@ -66,6 +66,7 @@ use {
     dashmap::DashMap,
     itertools::Itertools,
     log::*,
+    rand::Rng,
     rayon::{
         iter::{IntoParallelIterator, IntoParallelRefIterator, ParallelIterator},
         ThreadPool, ThreadPoolBuilder,
@@ -144,7 +145,7 @@ use {
         collections::{HashMap, HashSet},
         convert::{TryFrom, TryInto},
         fmt, mem,
-        ops::RangeInclusive,
+        ops::{Div, RangeInclusive},
         path::PathBuf,
         ptr,
         rc::Rc,
@@ -390,29 +391,32 @@ impl CachedExecutors {
             entry
         } else {
             saturating_add_assign!(self.stats.misses, 1);
-            if self.executors.len() >= self.max {
-                let mut least = u64::MAX;
-                let default_key = Pubkey::default();
-                let mut least_key = &default_key;
-
-                for (key, entry) in self.executors.iter() {
+            let mut counts = self
+                .executors
+                .iter()
+                .map(|(key, entry)| {
                     let count = entry.prev_epoch_count + entry.epoch_count.load(Relaxed);
-                    if count < least {
-                        least = count;
-                        least_key = key;
-                    }
+                    (key, count)
+                })
+                .collect::<Vec<_>>();
+            counts.sort_unstable_by_key(|(_, count)| *count);
+
+            let primer_count = Self::get_primer_count(counts.as_slice());
+
+            if self.executors.len() >= self.max {
+                if let Some(least_key) = counts.first().map(|least| *least.0) {
+                    let _ = self.executors.remove(&least_key);
+                    self.stats
+                        .evictions
+                        .entry(least_key)
+                        .and_modify(|c| saturating_add_assign!(*c, 1))
+                        .or_insert(1);
                 }
-                let least_key = *least_key;
-                let _ = self.executors.remove(&least_key);
-                self.stats
-                    .evictions
-                    .entry(least_key)
-                    .and_modify(|c| saturating_add_assign!(*c, 1))
-                    .or_insert(1);
             }
+
             CachedExecutorsEntry {
                 prev_epoch_count: 0,
-                epoch_count: AtomicU64::new(0),
+                epoch_count: AtomicU64::new(primer_count),
                 executor,
             }
         };
@@ -422,6 +426,38 @@ impl CachedExecutors {
     fn remove(&mut self, pubkey: &Pubkey) {
         let _ = self.executors.remove(pubkey);
     }
+
+    fn get_primer_count_upper_bound_inclusive(counts: &[(&Pubkey, u64)]) -> u64 {
+        const PRIMER_COUNT_TARGET_PERCENTILE: u64 = 85;
+        #[allow(clippy::assertions_on_constants)]
+        {
+            assert!(PRIMER_COUNT_TARGET_PERCENTILE <= 100);
+        }
+        // Executor use-frequencies are assumed to fit a Pareto distribution.  Choose an
+        // upper-bound for our primer count as the actual count at the target rank to avoid
+        // an upward bias
+
+        let target_index = u64::try_from(counts.len().saturating_sub(1))
+            .ok()
+            .and_then(|counts| {
+                let index = counts
+                    .saturating_mul(PRIMER_COUNT_TARGET_PERCENTILE)
+                    .div(100); // switch to u64::saturating_div once stable
+                usize::try_from(index).ok()
+            })
+            .unwrap_or(0);
+
+        counts
+            .get(target_index)
+            .map(|(_, count)| *count)
+            .unwrap_or(0)
+    }
+
+    fn get_primer_count(counts: &[(&Pubkey, u64)]) -> u64 {
+        let max_primer_count = Self::get_primer_count_upper_bound_inclusive(counts);
+        let mut rng = rand::thread_rng();
+        rng.gen_range(0, max_primer_count.saturating_add(1))
+    }
 }
 
 #[derive(Debug)]
@@ -12806,19 +12842,25 @@ pub(crate) mod tests {
         assert!(cache.get(&key1).is_some());
         assert!(cache.get(&key2).is_some());
         cache.put(&key4, executor.clone());
-        assert!(cache.get(&key1).is_some());
-        assert!(cache.get(&key2).is_some());
-        assert!(cache.get(&key3).is_none());
         assert!(cache.get(&key4).is_some());
+        let num_retained = [&key1, &key2, &key3]
+            .iter()
+            .map(|key| cache.get(key))
+            .flatten()
+            .count();
+        assert_eq!(num_retained, 2);
 
         assert!(cache.get(&key4).is_some());
         assert!(cache.get(&key4).is_some());
         assert!(cache.get(&key4).is_some());
         cache.put(&key3, executor.clone());
-        assert!(cache.get(&key1).is_some());
-        assert!(cache.get(&key2).is_none());
         assert!(cache.get(&key3).is_some());
-        assert!(cache.get(&key4).is_some());
+        let num_retained = [&key1, &key2, &key4]
+            .iter()
+            .map(|key| cache.get(key))
+            .flatten()
+            .count();
+        assert_eq!(num_retained, 2);
     }
 
     #[test]
@@ -12847,12 +12889,23 @@ pub(crate) mod tests {
         Arc::make_mut(&mut cache).put(&key4, executor.clone());
 
         assert!(cache.get(&key4).is_some());
-        assert!(cache.get(&key3).is_none());
+        let num_retained = [&key1, &key2, &key3]
+            .iter()
+            .map(|key| cache.get(key))
+            .flatten()
+            .count();
+        assert_eq!(num_retained, 2);
 
         Arc::make_mut(&mut cache).put(&key1, executor.clone());
         Arc::make_mut(&mut cache).put(&key3, executor.clone());
         assert!(cache.get(&key1).is_some());
-        assert!(cache.get(&key4).is_none());
+        assert!(cache.get(&key3).is_some());
+        let num_retained = [&key2, &key4]
+            .iter()
+            .map(|key| cache.get(key))
+            .flatten()
+            .count();
+        assert_eq!(num_retained, 1);
 
         cache = cache.clone_with_epoch(2);
         assert!(cache.current_epoch == 2);
@@ -15398,4 +15451,24 @@ pub(crate) mod tests {
             ))
         ));
     }
+
+    #[test]
+    fn test_executor_cache_get_primer_count_upper_bound_inclusive() {
+        let pubkey = Pubkey::default();
+        let v = [];
+        assert_eq!(
+            CachedExecutors::get_primer_count_upper_bound_inclusive(&v),
+            0
+        );
+        let v = [(&pubkey, 1)];
+        assert_eq!(
+            CachedExecutors::get_primer_count_upper_bound_inclusive(&v),
+            1
+        );
+        let v = (0u64..10).map(|i| (&pubkey, i)).collect::<Vec<_>>();
+        assert_eq!(
+            CachedExecutors::get_primer_count_upper_bound_inclusive(v.as_slice()),
+            7
+        );
+    }
 }