Home/Chain Registry/Block #285,181

Block #285,181

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 9:57:01 AM · Difficulty 9.9839 · 6,506,305 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dff38c711ca56a12e31405fbd03bb0028ee607ce37ed3a882b23918fb45ebfdd

View on Chainz ↗

Height

#285,181

Difficulty

9.983868

Transactions

Size

208 B

Version

Bits

09fbdec8

Nonce

2,690

Timestamp

11/30/2013, 9:57:01 AM

Confirmations

6,506,305

Merkle Root

5160ed8140b718951a81e30a9c571018d9888011ffde8bb59ad893d402a46bdc

Transactions (1)

Coinbase5160ed8140b718…d893d402a46bdc

1 in → 1 out10.0200 XPM116 B

AcLBm5Z9…S683d7c3

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.

6.779 × 10⁹⁸(99-digit number)

67793734787801203774…26417377275377931520

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

6.779 × 10⁹⁸(99-digit number)

67793734787801203774…26417377275377931519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.779 × 10⁹⁸(99-digit number)

67793734787801203774…26417377275377931521

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

1.355 × 10⁹⁹(100-digit number)

13558746957560240754…52834754550755863039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.355 × 10⁹⁹(100-digit number)

13558746957560240754…52834754550755863041

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

2.711 × 10⁹⁹(100-digit number)

27117493915120481509…05669509101511726079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.711 × 10⁹⁹(100-digit number)

27117493915120481509…05669509101511726081

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

5.423 × 10⁹⁹(100-digit number)

54234987830240963019…11339018203023452159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.423 × 10⁹⁹(100-digit number)

54234987830240963019…11339018203023452161

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

1.084 × 10¹⁰⁰(101-digit number)

10846997566048192603…22678036406046904319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.084 × 10¹⁰⁰(101-digit number)

10846997566048192603…22678036406046904321

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 285181

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 dff38c711ca56a12e31405fbd03bb0028ee607ce37ed3a882b23918fb45ebfdd

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 #285,181 on Chainz ↗