Home/Chain Registry/Block #2,378,287

Block #2,378,287

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/13/2017, 11:17:11 PM · Difficulty 10.8793 · 4,467,361 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

626296e81628645b1d15e9e5375953341dfa4ca9e31ec5937adb938dc61a1db8

View on Chainz ↗

Height

#2,378,287

Difficulty

10.879274

Transactions

Size

869 B

Version

Bits

0ae11813

Nonce

5,180,124

Timestamp

11/13/2017, 11:17:11 PM

Confirmations

4,467,361

Merkle Root

504ad5296e116a3d74cabf7fd0a82c6c43c3f7f21804894bd9d89364638b6e1a

Transactions (2)

Coinbase438e55a8d7a6cc…b5523ce0d48fe1

1 in → 1 out8.4500 XPM109 B

AbXsMkqC…RfzGXV9S

6be95a15528f2f…996fba9a8e5bd4

4 in → 2 out500.4932 XPM669 B

AJxd7sW2…ir1BcP6j ARiNwtFg…WsnNGDR9

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.

1.880 × 10⁹⁶(97-digit number)

18804156891527926346…96493238178620672000

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

1.880 × 10⁹⁶(97-digit number)

18804156891527926346…96493238178620671999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.880 × 10⁹⁶(97-digit number)

18804156891527926346…96493238178620672001

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

3.760 × 10⁹⁶(97-digit number)

37608313783055852693…92986476357241343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.760 × 10⁹⁶(97-digit number)

37608313783055852693…92986476357241344001

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

7.521 × 10⁹⁶(97-digit number)

75216627566111705386…85972952714482687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.521 × 10⁹⁶(97-digit number)

75216627566111705386…85972952714482688001

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

1.504 × 10⁹⁷(98-digit number)

15043325513222341077…71945905428965375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.504 × 10⁹⁷(98-digit number)

15043325513222341077…71945905428965376001

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

3.008 × 10⁹⁷(98-digit number)

30086651026444682154…43891810857930751999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.008 × 10⁹⁷(98-digit number)

30086651026444682154…43891810857930752001

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 2378287

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 626296e81628645b1d15e9e5375953341dfa4ca9e31ec5937adb938dc61a1db8

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 #2,378,287 on Chainz ↗

Block #2,378,287

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