Home/Chain Registry/Block #458,255

Block #458,255

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/24/2014, 11:18:23 AM · Difficulty 10.4213 · 6,336,153 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

84db89e09197c5072ac931a12eb13939a83085d11787faa194c887fcdf201ea3

View on Chainz ↗

Height

#458,255

Difficulty

10.421268

Transactions

Size

970 B

Version

Bits

0a6bd837

Nonce

125,482

Timestamp

3/24/2014, 11:18:23 AM

Confirmations

6,336,153

Merkle Root

1d4899deccb7c32cf80ef94b33ccf700447ce2fbfabc96b736d387a057bdf455

Transactions (1)

Coinbase1d4899deccb7c3…d387a057bdf455

1 in → 24 out9.1900 XPM879 B

AQvZBsUo…hppgRZTJ ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AJtNW28X…Syb4Ph5j AFutDVqJ…TJTJj6UF

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.

6.319 × 10⁹⁶(97-digit number)

63192087805264640194…09175498718217331000

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

6.319 × 10⁹⁶(97-digit number)

63192087805264640194…09175498718217330999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.319 × 10⁹⁶(97-digit number)

63192087805264640194…09175498718217331001

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

1.263 × 10⁹⁷(98-digit number)

12638417561052928038…18350997436434661999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.263 × 10⁹⁷(98-digit number)

12638417561052928038…18350997436434662001

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

2.527 × 10⁹⁷(98-digit number)

25276835122105856077…36701994872869323999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.527 × 10⁹⁷(98-digit number)

25276835122105856077…36701994872869324001

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

5.055 × 10⁹⁷(98-digit number)

50553670244211712155…73403989745738647999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.055 × 10⁹⁷(98-digit number)

50553670244211712155…73403989745738648001

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

1.011 × 10⁹⁸(99-digit number)

10110734048842342431…46807979491477295999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.011 × 10⁹⁸(99-digit number)

10110734048842342431…46807979491477296001

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 458255

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 84db89e09197c5072ac931a12eb13939a83085d11787faa194c887fcdf201ea3

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 #458,255 on Chainz ↗