Block #112,849

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/12/2013, 5:15:41 AM · Difficulty 9.7264 · 6,690,747 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cb91d018cd1682b506c3b8c54969c34978b3996dcb109747c88e13d59585536a

View on Chainz ↗

Height

#112,849

Difficulty

9.726413

Transactions

Size

2.74 KB

Version

Bits

09b9f62e

Nonce

214,102

Timestamp

8/12/2013, 5:15:41 AM

Confirmations

6,690,747

Mined by

⛏️ P2SHAKMPadN6bu5nUTyPzHMVVMXYKZJxrtnDQp

Merkle Root

8d064222eae1a20e33c9657336bb51d75db8932f233a90d229640b0d7d83536e

Transactions (2)

Coinbasedc9cb094a808fd…324e09c51d05a4

1 in → 1 out10.5800 XPM109 B

AKMPadN6…JxrtnDQp

90d669bec9961f…3700641311d7d3

21 in → 1 out171.0000 XPM2.55 KB

ARArVQTd…TbA6fDTa

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.

5.846 × 10⁹⁹(100-digit number)

58467094997735354241…93443752365305433489

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

5.846 × 10⁹⁹(100-digit number)

58467094997735354241…93443752365305433489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.846 × 10⁹⁹(100-digit number)

58467094997735354241…93443752365305433491

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

1.169 × 10¹⁰⁰(101-digit number)

11693418999547070848…86887504730610866979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.169 × 10¹⁰⁰(101-digit number)

11693418999547070848…86887504730610866981

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

2.338 × 10¹⁰⁰(101-digit number)

23386837999094141696…73775009461221733959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.338 × 10¹⁰⁰(101-digit number)

23386837999094141696…73775009461221733961

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

4.677 × 10¹⁰⁰(101-digit number)

46773675998188283393…47550018922443467919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.677 × 10¹⁰⁰(101-digit number)

46773675998188283393…47550018922443467921

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

9.354 × 10¹⁰⁰(101-digit number)

93547351996376566786…95100037844886935839

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