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Block #285,518

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 12:49:58 PM · Difficulty 9.9844 · 6,538,945 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a622bbed99a41d716e29395f83a3fff2c2b81b1da189164edf9b9a9ee933d401

View on Chainz ↗

Height

#285,518

Difficulty

9.984396

Transactions

Size

653 B

Version

Bits

09fc015a

Nonce

239,016

Timestamp

11/30/2013, 12:49:58 PM

Confirmations

6,538,945

Merkle Root

4f138da9b975b96be112e539e4bd4f12b68cdd430529b6e2e6eb4ba8751dee5f

Transactions (3)

Coinbase3ba9af436553db…d994c3c344ccd9

1 in → 1 out10.0400 XPM110 B

AeKNrjNj…1NEq95Ta

9a4e3af834902d…a3d9ad5744bfa7

1 in → 2 out5.8726 XPM226 B

ASJQsZFB…8WRBcBNd AMBaesuK…6AGZoQG4

970828b5d4a321…5065b146dde7c3

1 in → 2 out4.8220 XPM226 B

ATBnThzi…HE4jKpmw Abv8pzf1…t4zPXDTV

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.

1.408 × 10⁹⁶(97-digit number)

14088440412384598138…57140837307148492800

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

1.408 × 10⁹⁶(97-digit number)

14088440412384598138…57140837307148492799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.408 × 10⁹⁶(97-digit number)

14088440412384598138…57140837307148492801

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

2.817 × 10⁹⁶(97-digit number)

28176880824769196277…14281674614296985599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.817 × 10⁹⁶(97-digit number)

28176880824769196277…14281674614296985601

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

5.635 × 10⁹⁶(97-digit number)

56353761649538392555…28563349228593971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.635 × 10⁹⁶(97-digit number)

56353761649538392555…28563349228593971201

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

1.127 × 10⁹⁷(98-digit number)

11270752329907678511…57126698457187942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.127 × 10⁹⁷(98-digit number)

11270752329907678511…57126698457187942401

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

2.254 × 10⁹⁷(98-digit number)

22541504659815357022…14253396914375884799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 285518

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 a622bbed99a41d716e29395f83a3fff2c2b81b1da189164edf9b9a9ee933d401

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 #285,518 on Chainz ↗

Block #285,518

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