Home/Chain Registry/Block #453,592

Block #453,592

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 10:08:01 AM · Difficulty 10.3865 · 6,338,606 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0d0a766c9878efd05be5ac77d68c337d275c9950a2bca9fd73c824a190262d3e

View on Chainz ↗

Height

#453,592

Difficulty

10.386472

Transactions

Size

199 B

Version

Bits

0a62efd0

Nonce

327,505

Timestamp

3/21/2014, 10:08:01 AM

Confirmations

6,338,606

Merkle Root

8ebf09f461272a55f977d3c9327ab5f6fa8ab093735b98f62277cbf92ed4ce36

Transactions (1)

Coinbase8ebf09f461272a…77cbf92ed4ce36

1 in → 1 out9.2600 XPM109 B

ARASAFQZ…MNwky1f4

Prime Chain Origin

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

1.136 × 10⁹⁴(95-digit number)

11364000772125609149…63456422870594504640

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × 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 — Twin Prime Pair (origin ± 1)

origin − 1

1.136 × 10⁹⁴(95-digit number)

11364000772125609149…63456422870594504639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.136 × 10⁹⁴(95-digit number)

11364000772125609149…63456422870594504641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

2.272 × 10⁹⁴(95-digit number)

22728001544251218298…26912845741189009279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.272 × 10⁹⁴(95-digit number)

22728001544251218298…26912845741189009281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

4.545 × 10⁹⁴(95-digit number)

45456003088502436596…53825691482378018559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.545 × 10⁹⁴(95-digit number)

45456003088502436596…53825691482378018561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

9.091 × 10⁹⁴(95-digit number)

90912006177004873193…07651382964756037119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.091 × 10⁹⁴(95-digit number)

90912006177004873193…07651382964756037121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

1.818 × 10⁹⁵(96-digit number)

18182401235400974638…15302765929512074239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.818 × 10⁹⁵(96-digit number)

18182401235400974638…15302765929512074241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

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 — the large number shown above — 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 →

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — 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 − 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 453592

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 0d0a766c9878efd05be5ac77d68c337d275c9950a2bca9fd73c824a190262d3e

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 → Debug Window → 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 #453,592 on Chainz ↗