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Block #582,620

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/9/2014, 8:10:57 PM · Difficulty 10.9594 · 6,211,950 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d023fad05631ff10f848355c62bbf37e74a2ea29e3fbf23cd4ad2b002c58df63

View on Chainz ↗

Height

#582,620

Difficulty

10.959411

Transactions

Size

660 B

Version

Bits

0af59bfd

Nonce

260,269,176

Timestamp

6/9/2014, 8:10:57 PM

Confirmations

6,211,950

Merkle Root

4a7450c3ad579c72469533677d5c08a7a45b2355b0ac78ddb1f9a589694bb975

Transactions (3)

Coinbasea0f8df19bf4812…5156bd3c79e49b

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

641081a2d3ef75…62569267bd7509

1 in → 2 out6.6170 XPM225 B

AGdWVjRk…LFVsqCnK AJ8Uei7V…6exsRcPX

267a9ceb697cab…3ad9cd6919faf5

1 in → 2 out2.3827 XPM227 B

AS9ZCvju…bu3NEFwZ AVZhFG97…fgYSd4DX

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.

3.466 × 10¹⁰⁰(101-digit number)

34668680331584704853…56264590188156559360

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

3.466 × 10¹⁰⁰(101-digit number)

34668680331584704853…56264590188156559359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.466 × 10¹⁰⁰(101-digit number)

34668680331584704853…56264590188156559361

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

6.933 × 10¹⁰⁰(101-digit number)

69337360663169409706…12529180376313118719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.933 × 10¹⁰⁰(101-digit number)

69337360663169409706…12529180376313118721

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

1.386 × 10¹⁰¹(102-digit number)

13867472132633881941…25058360752626237439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.386 × 10¹⁰¹(102-digit number)

13867472132633881941…25058360752626237441

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

2.773 × 10¹⁰¹(102-digit number)

27734944265267763882…50116721505252474879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.773 × 10¹⁰¹(102-digit number)

27734944265267763882…50116721505252474881

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

5.546 × 10¹⁰¹(102-digit number)

55469888530535527765…00233443010504949759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.546 × 10¹⁰¹(102-digit number)

55469888530535527765…00233443010504949761

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 582620

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 d023fad05631ff10f848355c62bbf37e74a2ea29e3fbf23cd4ad2b002c58df63

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 #582,620 on Chainz ↗