Block #110,204

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/10/2013, 8:17:08 PM · Difficulty 9.6875 · 6,697,513 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

794c2f4416297cf4a6d646ebb8d6cabd4ef5010464cd9ac2ad46f0f386f6d4b3

View on Chainz ↗

Height

#110,204

Difficulty

9.687533

Transactions

Size

200 B

Version

Bits

09b00228

Nonce

188,260

Timestamp

8/10/2013, 8:17:08 PM

Confirmations

6,697,513

Mined by

⛏️ P2SHAczziGoaec4RPgvrGcUwYWvRLHdsHNtnSo

Merkle Root

82dd101ab027e35e4f6ee7a5e1f5b8017c80ffa30ef6c132c086b1bdcc82d014

Transactions (1)

Coinbase82dd101ab027e3…86b1bdcc82d014

1 in → 1 out10.6400 XPM109 B

AczziGoa…dsHNtnSo

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.

1.858 × 10⁹⁸(99-digit number)

18585729556035348022…69293694933294490719

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

1.858 × 10⁹⁸(99-digit number)

18585729556035348022…69293694933294490719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.858 × 10⁹⁸(99-digit number)

18585729556035348022…69293694933294490721

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

3.717 × 10⁹⁸(99-digit number)

37171459112070696044…38587389866588981439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.717 × 10⁹⁸(99-digit number)

37171459112070696044…38587389866588981441

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

7.434 × 10⁹⁸(99-digit number)

74342918224141392088…77174779733177962879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.434 × 10⁹⁸(99-digit number)

74342918224141392088…77174779733177962881

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

1.486 × 10⁹⁹(100-digit number)

14868583644828278417…54349559466355925759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.486 × 10⁹⁹(100-digit number)

14868583644828278417…54349559466355925761

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

2.973 × 10⁹⁹(100-digit number)

29737167289656556835…08699118932711851519

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 #110,204

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