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Block #2,662,421

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/15/2018, 5:39:53 PM · Difficulty 11.6419 · 4,178,103 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bca5d32abbf94b1886d6b6c2c2bae37068f5cbeee09ce1efdf3a73b6976f4475

View on Chainz ↗

Height

#2,662,421

Difficulty

11.641918

Transactions

Size

428 B

Version

Bits

0ba454b9

Nonce

1,308,084,832

Timestamp

5/15/2018, 5:39:53 PM

Confirmations

4,178,103

Merkle Root

bdf96b7a90dbeabde098d3f798bb5c7adb05c2a512a0d2c37d4637fa7372154e

Transactions (2)

Coinbasebf4a7aebef308d…89bb752181dea7

1 in → 1 out7.3800 XPM110 B

AZfVLbTK…X1Tw2pgq

0d6bf0945d09ff…efb5ff9bfbd1ed

1 in → 2 out226.2062 XPM226 B

AGrDd2SN…C7HcATuR ARJjetHj…kWTBsrkv

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.

4.555 × 10⁹⁸(99-digit number)

45553650565298723879…72759612831360614400

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

4.555 × 10⁹⁸(99-digit number)

45553650565298723879…72759612831360614399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.555 × 10⁹⁸(99-digit number)

45553650565298723879…72759612831360614401

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

9.110 × 10⁹⁸(99-digit number)

91107301130597447759…45519225662721228799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.110 × 10⁹⁸(99-digit number)

91107301130597447759…45519225662721228801

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

1.822 × 10⁹⁹(100-digit number)

18221460226119489551…91038451325442457599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.822 × 10⁹⁹(100-digit number)

18221460226119489551…91038451325442457601

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

3.644 × 10⁹⁹(100-digit number)

36442920452238979103…82076902650884915199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.644 × 10⁹⁹(100-digit number)

36442920452238979103…82076902650884915201

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

7.288 × 10⁹⁹(100-digit number)

72885840904477958207…64153805301769830399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.288 × 10⁹⁹(100-digit number)

72885840904477958207…64153805301769830401

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

1.457 × 10¹⁰⁰(101-digit number)

14577168180895591641…28307610603539660799

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 2662421

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 bca5d32abbf94b1886d6b6c2c2bae37068f5cbeee09ce1efdf3a73b6976f4475

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 #2,662,421 on Chainz ↗

Block #2,662,421

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