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Block #2,585,651

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/25/2018, 11:04:26 PM · Difficulty 11.2563 · 4,247,736 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ab7da4978944e07fb363398635d79c4017684b7a4c5bf617ecf6e4ea44648224

View on Chainz ↗

Height

#2,585,651

Difficulty

11.256269

Transactions

Size

574 B

Version

Bits

0b419ad7

Nonce

456,617,269

Timestamp

3/25/2018, 11:04:26 PM

Confirmations

4,247,736

Merkle Root

cfc53b169ab3388e4b685f289c7f2af3e5e1efbd2a51a61cd92a0b5f4aca3e62

Transactions (2)

Coinbased112d544097679…0bda3f9c1232dd

1 in → 1 out7.8900 XPM110 B

AJ12jsnF…cq5yhm9K

63854f8e38cd8e…c76a10a5b2007d

2 in → 2 out4.0421 XPM373 B

AMoVZvzA…kxjCyjNe AR62AXiY…LdAxrAxY

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.

3.611 × 10⁹⁶(97-digit number)

36111426813349561155…60524006164221936640

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

3.611 × 10⁹⁶(97-digit number)

36111426813349561155…60524006164221936639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.611 × 10⁹⁶(97-digit number)

36111426813349561155…60524006164221936641

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

7.222 × 10⁹⁶(97-digit number)

72222853626699122311…21048012328443873279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.222 × 10⁹⁶(97-digit number)

72222853626699122311…21048012328443873281

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

1.444 × 10⁹⁷(98-digit number)

14444570725339824462…42096024656887746559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.444 × 10⁹⁷(98-digit number)

14444570725339824462…42096024656887746561

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

2.888 × 10⁹⁷(98-digit number)

28889141450679648924…84192049313775493119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.888 × 10⁹⁷(98-digit number)

28889141450679648924…84192049313775493121

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

5.777 × 10⁹⁷(98-digit number)

57778282901359297849…68384098627550986239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.777 × 10⁹⁷(98-digit number)

57778282901359297849…68384098627550986241

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

1.155 × 10⁹⁸(99-digit number)

11555656580271859569…36768197255101972479

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 2585651

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 ab7da4978944e07fb363398635d79c4017684b7a4c5bf617ecf6e4ea44648224

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 #2,585,651 on Chainz ↗

Block #2,585,651

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