Home/Chain Registry/Block #2,478,075

Block #2,478,075

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/18/2018, 1:22:38 AM · Difficulty 10.9653 · 4,353,643 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3542b69312a3771df05127ef70bbafa5c64e09f7a0d180cd5b41561f0b4bbde8

View on Chainz ↗

Height

#2,478,075

Difficulty

10.965310

Transactions

Size

801 B

Version

Bits

0af71e8e

Nonce

255,004,691

Timestamp

1/18/2018, 1:22:38 AM

Confirmations

4,353,643

Merkle Root

fd49e2de0e1a060ab6b27f927ac70398a1cda127c75695f13984bd8f7c38641f

Transactions (3)

Coinbase216af1ac75cea2…46aa98b2e2ec1b

1 in → 1 out8.3200 XPM110 B

AVosYz6y…sYv63vKW

91dd4ef30a2897…31a15e706afd79

1 in → 2 out4.2157 XPM227 B

AdUnfZPJ…CfnSTpQz AeqNFTtn…yf1VNSpD

c3cca5a74f7d33…022e8888257fa3

2 in → 2 out5.1413 XPM373 B

AaUjgbny…KoYqKQYU AKM2ggG8…fZJ1wziC

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.

8.293 × 10⁹⁷(98-digit number)

82936563419049541342…68877998490235781120

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

8.293 × 10⁹⁷(98-digit number)

82936563419049541342…68877998490235781119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.293 × 10⁹⁷(98-digit number)

82936563419049541342…68877998490235781121

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

1.658 × 10⁹⁸(99-digit number)

16587312683809908268…37755996980471562239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.658 × 10⁹⁸(99-digit number)

16587312683809908268…37755996980471562241

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

3.317 × 10⁹⁸(99-digit number)

33174625367619816536…75511993960943124479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.317 × 10⁹⁸(99-digit number)

33174625367619816536…75511993960943124481

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

6.634 × 10⁹⁸(99-digit number)

66349250735239633073…51023987921886248959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.634 × 10⁹⁸(99-digit number)

66349250735239633073…51023987921886248961

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

1.326 × 10⁹⁹(100-digit number)

13269850147047926614…02047975843772497919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.326 × 10⁹⁹(100-digit number)

13269850147047926614…02047975843772497921

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 2478075

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 3542b69312a3771df05127ef70bbafa5c64e09f7a0d180cd5b41561f0b4bbde8

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 #2,478,075 on Chainz ↗

Block #2,478,075

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