Block #155,585

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/8/2013, 10:34:28 AM · Difficulty 9.8658 · 6,639,063 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

389045b15a04aa45855ea46fa5d961d7d64c965186deba5680a82863c7f17866

View on Chainz ↗

Height

#155,585

Difficulty

9.865757

Transactions

Size

573 B

Version

Bits

09dda242

Nonce

25,877

Timestamp

9/8/2013, 10:34:28 AM

Confirmations

6,639,063

Mined by

⛏️ P2SHARAURqjjHLd7LyRkcrLUGLPWkT44LhWTQj

Merkle Root

71964c99a5126783f42fc5c5a2d295eea4308798c8a745ee3811185568d596ad

Transactions (2)

Coinbasec3cf1dd7cde45d…8fbe55fdf6c740

1 in → 1 out10.2700 XPM109 B

ARAURqjj…44LhWTQj

a5c427f76302c2…b7cb47b4230bbf

2 in → 2 out2.0384 XPM373 B

AM3sBwmh…KpmiPeei AJFgYMoM…8k9Dx6qp

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.

4.617 × 10⁹⁷(98-digit number)

46172170179348634748…40519413726287446399

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

4.617 × 10⁹⁷(98-digit number)

46172170179348634748…40519413726287446399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.617 × 10⁹⁷(98-digit number)

46172170179348634748…40519413726287446401

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

9.234 × 10⁹⁷(98-digit number)

92344340358697269496…81038827452574892799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.234 × 10⁹⁷(98-digit number)

92344340358697269496…81038827452574892801

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

1.846 × 10⁹⁸(99-digit number)

18468868071739453899…62077654905149785599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.846 × 10⁹⁸(99-digit number)

18468868071739453899…62077654905149785601

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

3.693 × 10⁹⁸(99-digit number)

36937736143478907798…24155309810299571199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.693 × 10⁹⁸(99-digit number)

36937736143478907798…24155309810299571201

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

7.387 × 10⁹⁸(99-digit number)

73875472286957815597…48310619620599142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.387 × 10⁹⁸(99-digit number)

73875472286957815597…48310619620599142401

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