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Block #2,636,800

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/29/2018, 5:26:45 PM · Difficulty 11.4022 · 4,204,995 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e46a035e8ce429a563ceab57d65e83a9185769a336bac66ee1d72c29fb4dc0d2

View on Chainz ↗

Height

#2,636,800

Difficulty

11.402161

Transactions

Size

200 B

Version

Bits

0b66f404

Nonce

837,068,759

Timestamp

4/29/2018, 5:26:45 PM

Confirmations

4,204,995

Merkle Root

1a29bb4a23bbf77cdce6e215c5b9ca92c9730183071daaff39165ed3c91847c2

Transactions (1)

Coinbase1a29bb4a23bbf7…165ed3c91847c2

1 in → 1 out7.6800 XPM109 B

AHy5SEXb…LY7WgF7z

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.

1.483 × 10⁹⁷(98-digit number)

14836077483201966525…97580893509035505920

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

1.483 × 10⁹⁷(98-digit number)

14836077483201966525…97580893509035505919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.483 × 10⁹⁷(98-digit number)

14836077483201966525…97580893509035505921

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

2.967 × 10⁹⁷(98-digit number)

29672154966403933051…95161787018071011839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.967 × 10⁹⁷(98-digit number)

29672154966403933051…95161787018071011841

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

5.934 × 10⁹⁷(98-digit number)

59344309932807866103…90323574036142023679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.934 × 10⁹⁷(98-digit number)

59344309932807866103…90323574036142023681

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

1.186 × 10⁹⁸(99-digit number)

11868861986561573220…80647148072284047359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.186 × 10⁹⁸(99-digit number)

11868861986561573220…80647148072284047361

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

2.373 × 10⁹⁸(99-digit number)

23737723973123146441…61294296144568094719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.373 × 10⁹⁸(99-digit number)

23737723973123146441…61294296144568094721

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

4.747 × 10⁹⁸(99-digit number)

47475447946246292882…22588592289136189439

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 2636800

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 e46a035e8ce429a563ceab57d65e83a9185769a336bac66ee1d72c29fb4dc0d2

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 #2,636,800 on Chainz ↗

Block #2,636,800

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