Block #337,677

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 8:51:40 PM · Difficulty 10.1324 · 6,467,476 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d39c275e63a40fec223e9c08dff38852d968d202c98fc53f2036acb42517a9f6

View on Chainz ↗

Height

#337,677

Difficulty

10.132362

Transactions

Size

1.08 KB

Version

Bits

0a21e278

Nonce

150,690

Timestamp

12/31/2013, 8:51:40 PM

Confirmations

6,467,476

Mined by

⛏️ 'aR.?AQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

53256ee74d0692d6d636afd8f063564af9d1f83d03913e2e87780c89311133a9

Transactions (1)

Coinbase53256ee74d0692…780c89311133a9

1 in → 28 out9.7100 XPM1015 B

AQwRN8bE…V8PsTcY9 Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AQ8QAT3J…rCFKuVbR Acs9SHrk…QJSB8SFG

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.

2.152 × 10⁹⁷(98-digit number)

21523247900149744861…17269174032324690239

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

2.152 × 10⁹⁷(98-digit number)

21523247900149744861…17269174032324690239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.152 × 10⁹⁷(98-digit number)

21523247900149744861…17269174032324690241

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

4.304 × 10⁹⁷(98-digit number)

43046495800299489723…34538348064649380479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.304 × 10⁹⁷(98-digit number)

43046495800299489723…34538348064649380481

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

8.609 × 10⁹⁷(98-digit number)

86092991600598979447…69076696129298760959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.609 × 10⁹⁷(98-digit number)

86092991600598979447…69076696129298760961

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

1.721 × 10⁹⁸(99-digit number)

17218598320119795889…38153392258597521919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.721 × 10⁹⁸(99-digit number)

17218598320119795889…38153392258597521921

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

3.443 × 10⁹⁸(99-digit number)

34437196640239591779…76306784517195043839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.443 × 10⁹⁸(99-digit number)

34437196640239591779…76306784517195043841

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