Home/Chain Registry/Block #453,408

Block #453,408

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 7:02:43 AM · Difficulty 10.3869 · 6,338,554 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

955f12953e2618c6307e29a274b0e7953301592ae39cce3a7d7f2ee7f1c9748b

View on Chainz ↗

Height

#453,408

Difficulty

10.386917

Transactions

Size

1.90 KB

Version

Bits

0a630d02

Nonce

1,047,875

Timestamp

3/21/2014, 7:02:43 AM

Confirmations

6,338,554

Merkle Root

ee0b480587e48bd9a01e361049239966b763f77c920d6977f1fdab9032e5f96f

Transactions (3)

Coinbase986b337a3192c0…06b04048e22054

1 in → 1 out9.2800 XPM110 B

AeKNrjNj…1NEq95Ta

0d5c587e3cc840…fb97afa491bbb6

1 in → 2 out2147.8960 XPM225 B

AUzibHUX…MdPenjFJ AbZymyRQ…YZm38rjw

61effc6489f82e…dcca00f6298ef4

7 in → 21 out64.9700 XPM1.48 KB

AQizsfnX…n2pLZDBd Ad1Gcm3F…6jKhQUJt AdZKGbe9…j9mVS64K AQYQT37a…woJiw19q AebzNDsD…zaNsm1dg

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.

1.889 × 10⁹⁶(97-digit number)

18895852711356179942…20473893048788546560

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

1.889 × 10⁹⁶(97-digit number)

18895852711356179942…20473893048788546559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.889 × 10⁹⁶(97-digit number)

18895852711356179942…20473893048788546561

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

3.779 × 10⁹⁶(97-digit number)

37791705422712359884…40947786097577093119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.779 × 10⁹⁶(97-digit number)

37791705422712359884…40947786097577093121

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

7.558 × 10⁹⁶(97-digit number)

75583410845424719768…81895572195154186239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.558 × 10⁹⁶(97-digit number)

75583410845424719768…81895572195154186241

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

1.511 × 10⁹⁷(98-digit number)

15116682169084943953…63791144390308372479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.511 × 10⁹⁷(98-digit number)

15116682169084943953…63791144390308372481

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

3.023 × 10⁹⁷(98-digit number)

30233364338169887907…27582288780616744959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.023 × 10⁹⁷(98-digit number)

30233364338169887907…27582288780616744961

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 453408

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 955f12953e2618c6307e29a274b0e7953301592ae39cce3a7d7f2ee7f1c9748b

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 #453,408 on Chainz ↗