Block #113,427

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/12/2013, 1:04:58 PM · Difficulty 9.7322 · 6,703,161 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e5953fe971de8e0a77ca0754c23d0c5bc2085c9adbf86be51a08885fca602016

View on Chainz ↗

Height

#113,427

Difficulty

9.732161

Transactions

Size

201 B

Version

Bits

09bb6ee6

Nonce

44,500

Timestamp

8/12/2013, 1:04:58 PM

Confirmations

6,703,161

Mined by

⛏️ P2SHAKErQXMSbzQTkoT3CyUmWJvi8LJWgaCTzm

Merkle Root

6a3a9a76bfac3ec15bd47aa2b4e372d1229b5488cb9ead0e9463dd4a95723463

Transactions (1)

Coinbase6a3a9a76bfac3e…63dd4a95723463

1 in → 1 out10.5400 XPM109 B

AKErQXMS…JWgaCTzm

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.

2.347 × 10⁹⁸(99-digit number)

23476071924859528405…72201920963562369059

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

2.347 × 10⁹⁸(99-digit number)

23476071924859528405…72201920963562369059

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.347 × 10⁹⁸(99-digit number)

23476071924859528405…72201920963562369061

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

4.695 × 10⁹⁸(99-digit number)

46952143849719056811…44403841927124738119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.695 × 10⁹⁸(99-digit number)

46952143849719056811…44403841927124738121

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

9.390 × 10⁹⁸(99-digit number)

93904287699438113622…88807683854249476239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.390 × 10⁹⁸(99-digit number)

93904287699438113622…88807683854249476241

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

1.878 × 10⁹⁹(100-digit number)

18780857539887622724…77615367708498952479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.878 × 10⁹⁹(100-digit number)

18780857539887622724…77615367708498952481

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

3.756 × 10⁹⁹(100-digit number)

37561715079775245448…55230735416997904959

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 #113,427

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