Block #336,698

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 3:40:26 AM · Difficulty 10.1412 · 6,472,686 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

781ccac7d263f78aa36e7e3d92a624d7275d8910e649206825e467ed91b5a314

View on Chainz ↗

Height

#336,698

Difficulty

10.141239

Transactions

Size

1.05 KB

Version

Bits

0a24283b

Nonce

3,792

Timestamp

12/31/2013, 3:40:26 AM

Confirmations

6,472,686

Mined by

⛏️ :#aR<qjAac9Hjdgnw4T4L2csqLecJsmZjP4ktypc3

Merkle Root

70e963633ddca801c43aa72e4b347baa1dc9237bfb02eb39e1eca68a8e81d45a

Transactions (1)

Coinbase70e963633ddca8…eca68a8e81d45a

1 in → 27 out9.7100 XPM981 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR Ad9pSzHt…cpJ3y2zz AQwRN8bE…V8PsTcY9

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.

2.894 × 10⁹⁸(99-digit number)

28940252133783107338…21731778610482137609

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

2.894 × 10⁹⁸(99-digit number)

28940252133783107338…21731778610482137609

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.894 × 10⁹⁸(99-digit number)

28940252133783107338…21731778610482137611

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

5.788 × 10⁹⁸(99-digit number)

57880504267566214676…43463557220964275219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.788 × 10⁹⁸(99-digit number)

57880504267566214676…43463557220964275221

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

1.157 × 10⁹⁹(100-digit number)

11576100853513242935…86927114441928550439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.157 × 10⁹⁹(100-digit number)

11576100853513242935…86927114441928550441

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

2.315 × 10⁹⁹(100-digit number)

23152201707026485870…73854228883857100879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.315 × 10⁹⁹(100-digit number)

23152201707026485870…73854228883857100881

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

4.630 × 10⁹⁹(100-digit number)

46304403414052971741…47708457767714201759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.630 × 10⁹⁹(100-digit number)

46304403414052971741…47708457767714201761

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 #336,698

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