Home/Chain Registry/Block #546,064

Block #546,064

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/15/2014, 4:35:58 PM · Difficulty 10.9551 · 6,284,998 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

94833d3eb53fb7af70b547cfb22b0842e63e694f9f13f885c5c7ac944b13027f

View on Chainz ↗

Height

#546,064

Difficulty

10.955120

Transactions

Size

957 B

Version

Bits

0af482bb

Nonce

97,440,904

Timestamp

5/15/2014, 4:35:58 PM

Confirmations

6,284,998

Merkle Root

26ce10cd0cc74ea3576b3d8139e641a283f56c90fac38bd9451a9cd05dc14ef4

Transactions (3)

Coinbase417344cd19e92d…fd55a883251abe

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

9bb3e5612ecda9…bdb7caf7735312

3 in → 2 out5.1519 XPM523 B

ARpjHv1k…4F9NvuWN AUkmFDzd…Zk6yupt6

465cdc97219863…048b73e15bc183

1 in → 2 out0.6445 XPM225 B

AUpXXavy…DSkTfsUE AK9166NA…jA3Boio5

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.

1.020 × 10¹⁰¹(102-digit number)

10209216424935652912…06368951075453849600

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

1.020 × 10¹⁰¹(102-digit number)

10209216424935652912…06368951075453849599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.020 × 10¹⁰¹(102-digit number)

10209216424935652912…06368951075453849601

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

2.041 × 10¹⁰¹(102-digit number)

20418432849871305824…12737902150907699199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.041 × 10¹⁰¹(102-digit number)

20418432849871305824…12737902150907699201

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

4.083 × 10¹⁰¹(102-digit number)

40836865699742611649…25475804301815398399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.083 × 10¹⁰¹(102-digit number)

40836865699742611649…25475804301815398401

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

8.167 × 10¹⁰¹(102-digit number)

81673731399485223298…50951608603630796799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.167 × 10¹⁰¹(102-digit number)

81673731399485223298…50951608603630796801

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

1.633 × 10¹⁰²(103-digit number)

16334746279897044659…01903217207261593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.633 × 10¹⁰²(103-digit number)

16334746279897044659…01903217207261593601

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 546064

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 94833d3eb53fb7af70b547cfb22b0842e63e694f9f13f885c5c7ac944b13027f

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 #546,064 on Chainz ↗

Block #546,064

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