Block #15,193

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 6:49:57 PM · Difficulty 7.8458 · 6,779,370 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62c60bddd8a0e22101ea69673b98be80fb5f21d29b6ead50364e200b0041f8a6

View on Chainz ↗

Height

#15,193

Difficulty

7.845834

Transactions

Size

550 B

Version

Bits

07d88892

Nonce

1,551

Timestamp

7/11/2013, 6:49:57 PM

Confirmations

6,779,370

Mined by

⛏️ P2SHAc9yWhWrJ2Xd3wJ9oVrDkLucLTywuorNzG

Merkle Root

32b7ddc0600d34bd6ba5d794a17d90c1cc95e8463dca8506e70b59fd5b2081fb

Transactions (3)

Coinbasee88764082f18ea…d7db809881f9d2

1 in → 1 out16.2400 XPM108 B

Ac9yWhWr…ywuorNzG

1b690a1dda3604…1cd1b6a40195ef

1 in → 1 out19.4500 XPM191 B

APVvm9VV…TuzQ6EyW

6dab4aaaddc1e1…bce059df282f82

1 in → 1 out16.7100 XPM159 B

APabAd5V…YvtT2QCB

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.

3.356 × 10⁹⁹(100-digit number)

33561012329563497993…76898593365790915179

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

3.356 × 10⁹⁹(100-digit number)

33561012329563497993…76898593365790915179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.356 × 10⁹⁹(100-digit number)

33561012329563497993…76898593365790915181

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

6.712 × 10⁹⁹(100-digit number)

67122024659126995986…53797186731581830359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.712 × 10⁹⁹(100-digit number)

67122024659126995986…53797186731581830361

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

1.342 × 10¹⁰⁰(101-digit number)

13424404931825399197…07594373463163660719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.342 × 10¹⁰⁰(101-digit number)

13424404931825399197…07594373463163660721

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

2.684 × 10¹⁰⁰(101-digit number)

26848809863650798394…15188746926327321439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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