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Block #554,203

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/20/2014, 4:13:51 PM · Difficulty 10.9632 · 6,272,784 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

86487afb184ece28a48c6267e6a5e713a9fccbc95d7bf77cf80eb91e4acd2558

View on Chainz ↗

Height

#554,203

Difficulty

10.963153

Transactions

Size

660 B

Version

Bits

0af69132

Nonce

681,135,736

Timestamp

5/20/2014, 4:13:51 PM

Confirmations

6,272,784

Merkle Root

d72792a5af2434ee1ac48494c6d282f0cec146d1359d21b8e245d917fcc12812

Transactions (3)

Coinbase4ef17e3dab155e…aeb66fd8231c28

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

598d39e1b43c40…30280540de5356

1 in → 2 out5.6751 XPM226 B

AL4RdTaL…RQtoEqnD AM5GaTGS…k9AQNNQt

1912c18d4695d3…5ab522d56e4165

1 in → 2 out5.2053 XPM226 B

AYx4nLzA…D9yE3Min ATchn638…Fs5JotWM

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.

6.518 × 10⁹⁹(100-digit number)

65180138170668963100…82238925079404513280

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

6.518 × 10⁹⁹(100-digit number)

65180138170668963100…82238925079404513279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.518 × 10⁹⁹(100-digit number)

65180138170668963100…82238925079404513281

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

1.303 × 10¹⁰⁰(101-digit number)

13036027634133792620…64477850158809026559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.303 × 10¹⁰⁰(101-digit number)

13036027634133792620…64477850158809026561

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

2.607 × 10¹⁰⁰(101-digit number)

26072055268267585240…28955700317618053119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.607 × 10¹⁰⁰(101-digit number)

26072055268267585240…28955700317618053121

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

5.214 × 10¹⁰⁰(101-digit number)

52144110536535170480…57911400635236106239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.214 × 10¹⁰⁰(101-digit number)

52144110536535170480…57911400635236106241

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

1.042 × 10¹⁰¹(102-digit number)

10428822107307034096…15822801270472212479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.042 × 10¹⁰¹(102-digit number)

10428822107307034096…15822801270472212481

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 554203

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 86487afb184ece28a48c6267e6a5e713a9fccbc95d7bf77cf80eb91e4acd2558

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 #554,203 on Chainz ↗

Block #554,203

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