Home/Chain Registry/Block #547,393

Block #547,393

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/16/2014, 11:08:08 AM · Difficulty 10.9570 · 6,279,183 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6eda3ce3c6c17fde33218cf72cbb00fc136d843a02a4a0b816c0ba2a3fa8b7c0

View on Chainz ↗

Height

#547,393

Difficulty

10.957041

Transactions

Size

245 B

Version

Bits

0af500a8

Nonce

2,228,637,403

Timestamp

5/16/2014, 11:08:08 AM

Confirmations

6,279,183

Merkle Root

fc6af0ffea574d255337a65fe1609e4c985650f6acacbbc2b68bb834e7159322

Transactions (1)

Coinbasefc6af0ffea574d…8bb834e7159322

1 in → 2 out8.3200 XPM152 B

AaSwkwym…nTQKJ7bH ALPu3s2c…EJXLjVFh

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.

2.723 × 10¹⁰²(103-digit number)

27239660486960496647…66797821149343907840

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

2.723 × 10¹⁰²(103-digit number)

27239660486960496647…66797821149343907839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.723 × 10¹⁰²(103-digit number)

27239660486960496647…66797821149343907841

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

5.447 × 10¹⁰²(103-digit number)

54479320973920993295…33595642298687815679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.447 × 10¹⁰²(103-digit number)

54479320973920993295…33595642298687815681

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

1.089 × 10¹⁰³(104-digit number)

10895864194784198659…67191284597375631359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.089 × 10¹⁰³(104-digit number)

10895864194784198659…67191284597375631361

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

2.179 × 10¹⁰³(104-digit number)

21791728389568397318…34382569194751262719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.179 × 10¹⁰³(104-digit number)

21791728389568397318…34382569194751262721

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

4.358 × 10¹⁰³(104-digit number)

43583456779136794636…68765138389502525439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.358 × 10¹⁰³(104-digit number)

43583456779136794636…68765138389502525441

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 547393

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 6eda3ce3c6c17fde33218cf72cbb00fc136d843a02a4a0b816c0ba2a3fa8b7c0

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 #547,393 on Chainz ↗

Block #547,393

Cookie Preferences