Block #48,422

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 3:15:17 PM · Difficulty 8.8445 · 6,776,284 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f8921a5cbe14d3c8b53508ff7be9c40921e295136477eb2b8d6bd9d37506d2c

View on Chainz ↗

Height

#48,422

Difficulty

8.844477

Transactions

Size

703 B

Version

Bits

08d82f9e

Nonce

406

Timestamp

7/15/2013, 3:15:17 PM

Confirmations

6,776,284

Mined by

⛏️ P2SHAPvBFdS3MADCcCiTPEMjt5LT9PL419kB9V

Merkle Root

f576be9fe9b80766c02b2527d7fcca83456e20f2f10827bd1cf93b31c5f8f178

Transactions (2)

Coinbase79f11a5d52a74f…620b63958b820d

1 in → 1 out12.7800 XPM109 B

APvBFdS3…L419kB9V

bf1c16b43eda80…f9c8858e7dc8ef

4 in → 1 out62.6700 XPM499 B

AVNyAMwa…kKpeKorX

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.

1.626 × 10¹⁰⁷(108-digit number)

16265689181340668648…93747156965115275859

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

1.626 × 10¹⁰⁷(108-digit number)

16265689181340668648…93747156965115275859

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.626 × 10¹⁰⁷(108-digit number)

16265689181340668648…93747156965115275861

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

3.253 × 10¹⁰⁷(108-digit number)

32531378362681337296…87494313930230551719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.253 × 10¹⁰⁷(108-digit number)

32531378362681337296…87494313930230551721

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

6.506 × 10¹⁰⁷(108-digit number)

65062756725362674592…74988627860461103439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.506 × 10¹⁰⁷(108-digit number)

65062756725362674592…74988627860461103441

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

1.301 × 10¹⁰⁸(109-digit number)

13012551345072534918…49977255720922206879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.301 × 10¹⁰⁸(109-digit number)

13012551345072534918…49977255720922206881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #48,422

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