Block #336,890

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/31/2013, 7:03:56 AM · Difficulty 10.1397 · 6,458,545 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2b2026cc31fb3ad8852f38287870a84779940f2952a0b7cad13298c21016114a

View on Chainz ↗

Height

#336,890

Difficulty

10.139711

Transactions

Size

1.12 KB

Version

Bits

0a23c416

Nonce

452,706

Timestamp

12/31/2013, 7:03:56 AM

Confirmations

6,458,545

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9ec476fa499cd9185ee7146ffbe3327d8038e8ca2dcb2685667204b6b4fbe839

Transactions (5)

Coinbase0530996478bb77…5216a43ecd049e

1 in → 1 out9.7569 XPM110 B

AeKNrjNj…1NEq95Ta

ce24de2d0da92b…8985ca585760fe

1 in → 1 out9.6700 XPM158 B

AUQWNLX2…FxwsS5kV

d1167062ed5b2d…0dd8a7b4651b2e

2 in → 1 out0.5000 XPM339 B

AV7734xX…G1j8VGMs

bf039e4e43ffab…53faff71196483

1 in → 2 out4.5146 XPM226 B

AXxp24rY…yi3yUFBu AW25QDp3…oF5YKRfe

3b315731d4f538…35475ccb66a8f3

1 in → 2 out3.3247 XPM225 B

AbQLVA4y…UTMRhx41 AUfZs9KH…a4h5GYWM

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.

1.925 × 10⁹³(94-digit number)

19258766638707498728…97833855079504314639

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

1.925 × 10⁹³(94-digit number)

19258766638707498728…97833855079504314639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.925 × 10⁹³(94-digit number)

19258766638707498728…97833855079504314641

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

3.851 × 10⁹³(94-digit number)

38517533277414997456…95667710159008629279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.851 × 10⁹³(94-digit number)

38517533277414997456…95667710159008629281

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

7.703 × 10⁹³(94-digit number)

77035066554829994912…91335420318017258559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.703 × 10⁹³(94-digit number)

77035066554829994912…91335420318017258561

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

1.540 × 10⁹⁴(95-digit number)

15407013310965998982…82670840636034517119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.540 × 10⁹⁴(95-digit number)

15407013310965998982…82670840636034517121

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

3.081 × 10⁹⁴(95-digit number)

30814026621931997964…65341681272069034239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.081 × 10⁹⁴(95-digit number)

30814026621931997964…65341681272069034241

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