Home/Chain Registry/Block #2,457,085

Block #2,457,085

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/4/2018, 10:18:38 AM · Difficulty 10.9538 · 4,384,879 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0cdbdbe1baa02a853c1e1907c784a96aae8aa0e8a97fe76044f5ba2b57b79ba5

View on Chainz ↗

Height

#2,457,085

Difficulty

10.953787

Transactions

Size

723 B

Version

Bits

0af42b5e

Nonce

303,364,163

Timestamp

1/4/2018, 10:18:38 AM

Confirmations

4,384,879

Merkle Root

ab00f743fb1f74c595bff6c23709747a90d83caff88193fae2dd55d82013c86b

Transactions (2)

Coinbase2a3cdd353fd9f3…c9b6b77c78ff0a

1 in → 1 out8.3300 XPM110 B

AHewudHd…k6BTMtac

1df4ace792816c…e3b878c8ed63f5

3 in → 2 out2957.3221 XPM523 B

AaftQQdL…VsnTsiXY AJGk8uJk…JvHmET2f

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.

6.847 × 10⁹⁴(95-digit number)

68479910011170024075…76416777720187821200

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

6.847 × 10⁹⁴(95-digit number)

68479910011170024075…76416777720187821199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.847 × 10⁹⁴(95-digit number)

68479910011170024075…76416777720187821201

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

1.369 × 10⁹⁵(96-digit number)

13695982002234004815…52833555440375642399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.369 × 10⁹⁵(96-digit number)

13695982002234004815…52833555440375642401

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

2.739 × 10⁹⁵(96-digit number)

27391964004468009630…05667110880751284799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.739 × 10⁹⁵(96-digit number)

27391964004468009630…05667110880751284801

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

5.478 × 10⁹⁵(96-digit number)

54783928008936019260…11334221761502569599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.478 × 10⁹⁵(96-digit number)

54783928008936019260…11334221761502569601

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

1.095 × 10⁹⁶(97-digit number)

10956785601787203852…22668443523005139199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.095 × 10⁹⁶(97-digit number)

10956785601787203852…22668443523005139201

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.191 × 10⁹⁶(97-digit number)

21913571203574407704…45336887046010278399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2457085

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 0cdbdbe1baa02a853c1e1907c784a96aae8aa0e8a97fe76044f5ba2b57b79ba5

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 #2,457,085 on Chainz ↗

Block #2,457,085

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