XPM Prime Explorer symbol
XPMPrime Explorer
Home/Chain Registry/Block #453,189

Block #453,189

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 3/21/2014, 2:27:53 AM Β· Difficulty 10.3927 Β· 6,390,138 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
93c4456a763b1448dc57b57f3d9f29e0c5fc62c8a01303d1f8e1a42fed72b716
View on Chainz β†—

Height

#453,189

Difficulty

10.392743

Transactions

1

Size

208 B

Version

2

Bits

0a648ac9

Nonce

808

Timestamp

3/21/2014, 2:27:53 AM

Confirmations

6,390,138

Merkle Root

cd648ab0fb48de1f7dd19f80f8183652a58a22b6afeb022b2a6f8b7b07fdd036
Transactions (1)
Coinbasecd648ab0fb48de…6f8b7b07fdd036
1 in β†’ 1 out9.2400 XPM116 B
AbwWkWZt…kawDhufa
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.792 Γ— 10⁹⁹(100-digit number)
17922149436458483975…88470933629443568960
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.792 Γ— 10⁹⁹(100-digit number)
17922149436458483975…88470933629443568959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.792 Γ— 10⁹⁹(100-digit number)
17922149436458483975…88470933629443568961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
3.584 Γ— 10⁹⁹(100-digit number)
35844298872916967950…76941867258887137919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.584 Γ— 10⁹⁹(100-digit number)
35844298872916967950…76941867258887137921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
7.168 Γ— 10⁹⁹(100-digit number)
71688597745833935900…53883734517774275839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.168 Γ— 10⁹⁹(100-digit number)
71688597745833935900…53883734517774275841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.433 Γ— 10¹⁰⁰(101-digit number)
14337719549166787180…07767469035548551679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.433 Γ— 10¹⁰⁰(101-digit number)
14337719549166787180…07767469035548551681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
2.867 Γ— 10¹⁰⁰(101-digit number)
28675439098333574360…15534938071097103359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.867 Γ— 10¹⁰⁰(101-digit number)
28675439098333574360…15534938071097103361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 453189

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 93c4456a763b1448dc57b57f3d9f29e0c5fc62c8a01303d1f8e1a42fed72b716

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #453,189 on Chainz β†—
Circulating Supply:57,990,977 XPMΒ·at block #6,843,326 Β· updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy PolicyΒ·
AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

Β·Privacy Policy