Block #300,731

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 6:21:01 PM · Difficulty 9.9924 · 6,506,478 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d74ad7408f85d77c9e5ff57662f63ccc6c8aede02dee8edbcb91039d10db81dc

View on Chainz ↗

Height

#300,731

Difficulty

9.992388

Transactions

Size

1.18 KB

Version

Bits

09fe0d25

Nonce

622

Timestamp

12/8/2013, 6:21:01 PM

Confirmations

6,506,478

Mined by

⛏️ aRAYtDvcGsMH2GY5bD4Hc2rArhMdVuAcA7m7

Merkle Root

9944c40d89b11c3ccd10ada48d365908604ee9e32a6a8e57a934d8abe1818066

Transactions (1)

Coinbase9944c40d89b11c…34d8abe1818066

1 in → 31 out9.9800 XPM1.09 KB

AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AXNGJQx4…d9FM96S4 AaZZSQ1Q…L4KtW8Rb AdJit5uN…JD6UuauU

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.

5.758 × 10⁹⁹(100-digit number)

57580839610175162339…38492500396097029119

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

5.758 × 10⁹⁹(100-digit number)

57580839610175162339…38492500396097029119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.758 × 10⁹⁹(100-digit number)

57580839610175162339…38492500396097029121

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

1.151 × 10¹⁰⁰(101-digit number)

11516167922035032467…76985000792194058239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.151 × 10¹⁰⁰(101-digit number)

11516167922035032467…76985000792194058241

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

2.303 × 10¹⁰⁰(101-digit number)

23032335844070064935…53970001584388116479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.303 × 10¹⁰⁰(101-digit number)

23032335844070064935…53970001584388116481

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

4.606 × 10¹⁰⁰(101-digit number)

46064671688140129871…07940003168776232959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.606 × 10¹⁰⁰(101-digit number)

46064671688140129871…07940003168776232961

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

9.212 × 10¹⁰⁰(101-digit number)

92129343376280259743…15880006337552465919

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #300,731

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