Block #484,033

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/10/2014, 8:52:50 AM · Difficulty 10.5759 · 6,326,830 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

21ac75b08a6564a6f9dc9e1abd741836ae5f1a5556889ab0843503596eaecd44

View on Chainz ↗

Height

#484,033

Difficulty

10.575904

Transactions

Size

1.30 KB

Version

Bits

0a936e6c

Nonce

24,835

Timestamp

4/10/2014, 8:52:50 AM

Confirmations

6,326,830

Mined by

⛏️ bLAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

fd2dc9fa4c036a909ddb0a3bf5377a701511c08818a0eaaa869395fb21d91cdb

Transactions (3)

Coinbase4fb2fa6ca2976c…513de5e1d7293c

1 in → 17 out8.9500 XPM641 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AdFLJFhb…bsaVkAyh ASgUri65…C7NLcyBg AGz9gyZW…bo8NYQpw

c0be028df00980…fa536acc7d0618

2 in → 2 out1.9912 XPM374 B

AbkFb3wH…bdfcDGtR AXXpBF7U…HdGrokcT

4cad5c99f13240…57f7182c92bf84

1 in → 2 out7.9987 XPM226 B

AZy4McFD…bwxbjsgd AWhqCNs1…mTz9bU71

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.

4.067 × 10⁹⁹(100-digit number)

40676660764479878665…22353541628711720959

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

4.067 × 10⁹⁹(100-digit number)

40676660764479878665…22353541628711720959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.067 × 10⁹⁹(100-digit number)

40676660764479878665…22353541628711720961

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

8.135 × 10⁹⁹(100-digit number)

81353321528959757330…44707083257423441919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.135 × 10⁹⁹(100-digit number)

81353321528959757330…44707083257423441921

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

1.627 × 10¹⁰⁰(101-digit number)

16270664305791951466…89414166514846883839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.627 × 10¹⁰⁰(101-digit number)

16270664305791951466…89414166514846883841

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

3.254 × 10¹⁰⁰(101-digit number)

32541328611583902932…78828333029693767679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.254 × 10¹⁰⁰(101-digit number)

32541328611583902932…78828333029693767681

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

6.508 × 10¹⁰⁰(101-digit number)

65082657223167805864…57656666059387535359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.508 × 10¹⁰⁰(101-digit number)

65082657223167805864…57656666059387535361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Cross-reference on Chainz Explorer

Block #484,033

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