Block #137,576

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/27/2013, 9:28:26 PM · Difficulty 9.8225 · 6,671,387 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

294abe3c43d49699dca3aa5309c224a50c72e20616c220cbb60e6af7b41d8d0a

View on Chainz ↗

Height

#137,576

Difficulty

9.822499

Transactions

Size

357 B

Version

Bits

09d28f53

Nonce

462,906

Timestamp

8/27/2013, 9:28:26 PM

Confirmations

6,671,387

Mined by

⛏️ P2SHAT3dRckguQx6f5eEEVjWX7iYBwiggfceho

Merkle Root

2641b67d7465fd8fa247962b86e7789f6115b97ae20bb78c8522f3eac09d39e1

Transactions (2)

Coinbase96245c07867258…8a8b94f834963f

1 in → 1 out10.3600 XPM109 B

AT3dRckg…iggfceho

9e624d8b1b0730…986e28c1bed09b

1 in → 1 out10.5000 XPM159 B

AZXETrNV…4pNkP86v

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.

6.160 × 10⁹²(93-digit number)

61602951545515984818…97368408027902405079

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

6.160 × 10⁹²(93-digit number)

61602951545515984818…97368408027902405079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.160 × 10⁹²(93-digit number)

61602951545515984818…97368408027902405081

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

1.232 × 10⁹³(94-digit number)

12320590309103196963…94736816055804810159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.232 × 10⁹³(94-digit number)

12320590309103196963…94736816055804810161

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

2.464 × 10⁹³(94-digit number)

24641180618206393927…89473632111609620319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.464 × 10⁹³(94-digit number)

24641180618206393927…89473632111609620321

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

4.928 × 10⁹³(94-digit number)

49282361236412787854…78947264223219240639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.928 × 10⁹³(94-digit number)

49282361236412787854…78947264223219240641

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

9.856 × 10⁹³(94-digit number)

98564722472825575709…57894528446438481279

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 #137,576

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