Home/Chain Registry/Block #455,046

Block #455,046

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 8:16:10 AM · Difficulty 10.4020 · 6,336,440 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef1a23976cfffc45612c5e7f7df1578764a91ae10c59aaa8400a9e98e6938b17

View on Chainz ↗

Height

#455,046

Difficulty

10.401994

Transactions

Size

208 B

Version

Bits

0a66e910

Nonce

39,312

Timestamp

3/22/2014, 8:16:10 AM

Confirmations

6,336,440

Merkle Root

64328dd71547618472fb2b4377c9b7a9c616f7ac4fac7a97656352a8b7fd3e7b

Transactions (1)

Coinbase64328dd7154761…6352a8b7fd3e7b

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

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.

2.471 × 10⁹⁸(99-digit number)

24714579397415666617…77781015708287968280

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

2.471 × 10⁹⁸(99-digit number)

24714579397415666617…77781015708287968279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.471 × 10⁹⁸(99-digit number)

24714579397415666617…77781015708287968281

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

4.942 × 10⁹⁸(99-digit number)

49429158794831333235…55562031416575936559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.942 × 10⁹⁸(99-digit number)

49429158794831333235…55562031416575936561

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

9.885 × 10⁹⁸(99-digit number)

98858317589662666470…11124062833151873119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.885 × 10⁹⁸(99-digit number)

98858317589662666470…11124062833151873121

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

1.977 × 10⁹⁹(100-digit number)

19771663517932533294…22248125666303746239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.977 × 10⁹⁹(100-digit number)

19771663517932533294…22248125666303746241

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

3.954 × 10⁹⁹(100-digit number)

39543327035865066588…44496251332607492479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.954 × 10⁹⁹(100-digit number)

39543327035865066588…44496251332607492481

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 455046

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 ef1a23976cfffc45612c5e7f7df1578764a91ae10c59aaa8400a9e98e6938b17

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 #455,046 on Chainz ↗