Home/Chain Registry/Block #2,854,267

Block #2,854,267

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/25/2018, 7:09:08 AM · Difficulty 11.7098 · 3,985,968 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ebbf50fd5d3bfb98209b1f24f48d0ffd64c252e0016b6316fbc8c331d4cb495d

View on Chainz ↗

Height

#2,854,267

Difficulty

11.709801

Transactions

Size

6.05 KB

Version

Bits

0bb5b58d

Nonce

1,625,651,470

Timestamp

9/25/2018, 7:09:08 AM

Confirmations

3,985,968

Merkle Root

848d18fbeb17491b75c867b96ae58c098cfd32d9fb9621e807c490aa2e5f419b

Transactions (2)

Coinbase7d2a9b30cfa728…d437e620c4fe04

1 in → 1 out7.3700 XPM109 B

ALQGpaT6…9dLVU1B9

59445931caf751…31cafef4606d9d

40 in → 2 out617.9814 XPM5.85 KB

AT2ZqrhV…zrdzQgZb ASKzMvCy…cVvboEtV

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.

2.097 × 10⁹²(93-digit number)

20979694225649498088…46305408366829521280

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

2.097 × 10⁹²(93-digit number)

20979694225649498088…46305408366829521279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.097 × 10⁹²(93-digit number)

20979694225649498088…46305408366829521281

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

4.195 × 10⁹²(93-digit number)

41959388451298996176…92610816733659042559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.195 × 10⁹²(93-digit number)

41959388451298996176…92610816733659042561

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

8.391 × 10⁹²(93-digit number)

83918776902597992352…85221633467318085119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.391 × 10⁹²(93-digit number)

83918776902597992352…85221633467318085121

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

1.678 × 10⁹³(94-digit number)

16783755380519598470…70443266934636170239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.678 × 10⁹³(94-digit number)

16783755380519598470…70443266934636170241

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

3.356 × 10⁹³(94-digit number)

33567510761039196941…40886533869272340479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.356 × 10⁹³(94-digit number)

33567510761039196941…40886533869272340481

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

6.713 × 10⁹³(94-digit number)

67135021522078393882…81773067738544680959

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 2854267

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 ebbf50fd5d3bfb98209b1f24f48d0ffd64c252e0016b6316fbc8c331d4cb495d

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 #2,854,267 on Chainz ↗

Block #2,854,267

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