Home/Chain Registry/Block #2,781,288

Block #2,781,288

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/6/2018, 5:48:23 AM · Difficulty 11.6503 · 4,062,633 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f7ef10dcded0c73ac9b33d6fbe2ec852f5163b837d35b74bd97bfb7685670d57

View on Chainz ↗

Height

#2,781,288

Difficulty

11.650258

Transactions

Size

1.51 KB

Version

Bits

0ba6774a

Nonce

491,706,081

Timestamp

8/6/2018, 5:48:23 AM

Confirmations

4,062,633

Merkle Root

82e062dcc88ddea6197e8d38c106b1fb75b7e27088a86ea3bd274f532e1759b2

Transactions (3)

Coinbase2d5ed25d7398ec…70ae6e60b8b8e6

1 in → 1 out7.3800 XPM109 B

AZtxQr2F…7grUWrUz

cfbcace8e1f0a3…3a8dd5faf3f250

7 in → 2 out30.1568 XPM977 B

ANz65jvR…vu7Ymacm ASqqyVtj…nzvAKb8a

8cbffde66194a1…a7e6575e833b86

2 in → 2 out5.0726 XPM372 B

ALRJaAkL…A6DXwV2C AbJVNz8f…Sn9Aq29V

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.

7.933 × 10⁹⁴(95-digit number)

79331620433841169104…70822896392180860720

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

7.933 × 10⁹⁴(95-digit number)

79331620433841169104…70822896392180860719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.933 × 10⁹⁴(95-digit number)

79331620433841169104…70822896392180860721

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

1.586 × 10⁹⁵(96-digit number)

15866324086768233820…41645792784361721439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.586 × 10⁹⁵(96-digit number)

15866324086768233820…41645792784361721441

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

3.173 × 10⁹⁵(96-digit number)

31732648173536467641…83291585568723442879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.173 × 10⁹⁵(96-digit number)

31732648173536467641…83291585568723442881

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

6.346 × 10⁹⁵(96-digit number)

63465296347072935283…66583171137446885759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.346 × 10⁹⁵(96-digit number)

63465296347072935283…66583171137446885761

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

1.269 × 10⁹⁶(97-digit number)

12693059269414587056…33166342274893771519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.269 × 10⁹⁶(97-digit number)

12693059269414587056…33166342274893771521

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

2.538 × 10⁹⁶(97-digit number)

25386118538829174113…66332684549787543039

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 2781288

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 f7ef10dcded0c73ac9b33d6fbe2ec852f5163b837d35b74bd97bfb7685670d57

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 #2,781,288 on Chainz ↗

Block #2,781,288

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