Block #113,508

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/12/2013, 2:16:49 PM · Difficulty 9.7327 · 6,703,682 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6435b54f6e75d47c8bda827590d959f13b7f30990acdd69b78e597e9c537ea5b

View on Chainz ↗

Height

#113,508

Difficulty

9.732679

Transactions

Size

473 B

Version

Bits

09bb90d4

Nonce

229,173

Timestamp

8/12/2013, 2:16:49 PM

Confirmations

6,703,682

Mined by

⛏️ P2SHAKErQXMSbzQTkoT3CyUmWJvi8LJWgaCTzm

Merkle Root

24c35510980aded9081cd3e5ea6190f9d5ae01798c2ed90c6560bd7e894a8218

Transactions (2)

Coinbased2b2aa95aefcb3…da1461c5f32988

1 in → 1 out10.5500 XPM109 B

AKErQXMS…JWgaCTzm

1e89feba9fed6a…4b2fd64a559750

2 in → 1 out22.9000 XPM273 B

AbnmJJMR…NWjrwYRj

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.

2.801 × 10⁹⁷(98-digit number)

28010862007375960595…32174308600437437879

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

2.801 × 10⁹⁷(98-digit number)

28010862007375960595…32174308600437437879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.801 × 10⁹⁷(98-digit number)

28010862007375960595…32174308600437437881

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

5.602 × 10⁹⁷(98-digit number)

56021724014751921191…64348617200874875759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.602 × 10⁹⁷(98-digit number)

56021724014751921191…64348617200874875761

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

1.120 × 10⁹⁸(99-digit number)

11204344802950384238…28697234401749751519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.120 × 10⁹⁸(99-digit number)

11204344802950384238…28697234401749751521

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

2.240 × 10⁹⁸(99-digit number)

22408689605900768476…57394468803499503039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.240 × 10⁹⁸(99-digit number)

22408689605900768476…57394468803499503041

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

4.481 × 10⁹⁸(99-digit number)

44817379211801536952…14788937606999006079

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 #113,508

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