Block #304,813

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/11/2013, 3:20:29 AM · Difficulty 9.9934 · 6,502,354 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

10e022f60c4ab70422bdf97f6b5ce6d189a2a501fd3959d9f6dfb7f5c9ae970c

View on Chainz ↗

Height

#304,813

Difficulty

9.993447

Transactions

Size

1.11 KB

Version

Bits

09fe5283

Nonce

13,790

Timestamp

12/11/2013, 3:20:29 AM

Confirmations

6,502,354

Mined by

⛏️ aRAd9pSzHtZ9ebPysWxo4VY8quTmcpJ3y2zz

Merkle Root

0a1fce4816275515a1ee12f98856dd1fde818c4b16612a4e18a9c9ed2c897faa

Transactions (1)

Coinbase0a1fce48162755…a9c9ed2c897faa

1 in → 29 out9.9800 XPM1.02 KB

Ad9pSzHt…cpJ3y2zz AYcLTeXR…bscgPops AGPYJBwg…5yWMRKmU Ae6gEbs5…m5Mn8oYw ARzXge7S…CEjL5oYm

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.

9.192 × 10⁹¹(92-digit number)

91921407816682212372…61898436776374957359

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

9.192 × 10⁹¹(92-digit number)

91921407816682212372…61898436776374957359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.192 × 10⁹¹(92-digit number)

91921407816682212372…61898436776374957361

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

1.838 × 10⁹²(93-digit number)

18384281563336442474…23796873552749914719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.838 × 10⁹²(93-digit number)

18384281563336442474…23796873552749914721

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

3.676 × 10⁹²(93-digit number)

36768563126672884949…47593747105499829439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.676 × 10⁹²(93-digit number)

36768563126672884949…47593747105499829441

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

7.353 × 10⁹²(93-digit number)

73537126253345769898…95187494210999658879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.353 × 10⁹²(93-digit number)

73537126253345769898…95187494210999658881

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

1.470 × 10⁹³(94-digit number)

14707425250669153979…90374988421999317759

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 #304,813

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