Home/Chain Registry/Block #572,594

Block #572,594

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/2/2014, 5:00:36 AM · Difficulty 10.9661 · 6,254,580 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4cd27fc58c3309f3f919aa78748b9f0147424aa4d56d09f86a6e87c096076e86

View on Chainz ↗

Height

#572,594

Difficulty

10.966144

Transactions

Size

660 B

Version

Bits

0af7553b

Nonce

231,877,241

Timestamp

6/2/2014, 5:00:36 AM

Confirmations

6,254,580

Merkle Root

0d863a37f54d7ec945951a911b785c67d09c87d5592ab687be3947e5ce131876

Transactions (3)

Coinbaseb49c8b271ddadf…12c5575007726f

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

841e449a797f6e…ebb328e4f91734

1 in → 2 out3.1850 XPM226 B

AXi1UdPG…k5oQddYi ATjwywoV…ga9eRXwi

f584fdfb8a2994…d957c85c1c6cbd

1 in → 2 out3.0777 XPM225 B

AVSSoqRA…aFjFn3Zm AUh3KJJj…zd2SsM1P

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.

2.378 × 10¹⁰¹(102-digit number)

23783033456493004381…96074411181248716800

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

2.378 × 10¹⁰¹(102-digit number)

23783033456493004381…96074411181248716799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.378 × 10¹⁰¹(102-digit number)

23783033456493004381…96074411181248716801

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

4.756 × 10¹⁰¹(102-digit number)

47566066912986008763…92148822362497433599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.756 × 10¹⁰¹(102-digit number)

47566066912986008763…92148822362497433601

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

9.513 × 10¹⁰¹(102-digit number)

95132133825972017527…84297644724994867199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.513 × 10¹⁰¹(102-digit number)

95132133825972017527…84297644724994867201

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

1.902 × 10¹⁰²(103-digit number)

19026426765194403505…68595289449989734399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.902 × 10¹⁰²(103-digit number)

19026426765194403505…68595289449989734401

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

3.805 × 10¹⁰²(103-digit number)

38052853530388807011…37190578899979468799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.805 × 10¹⁰²(103-digit number)

38052853530388807011…37190578899979468801

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.610 × 10¹⁰²(103-digit number)

76105707060777614022…74381157799958937599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 572594

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 4cd27fc58c3309f3f919aa78748b9f0147424aa4d56d09f86a6e87c096076e86

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 #572,594 on Chainz ↗

Block #572,594

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