Block #22,626

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 5:48:05 PM · Difficulty 7.9538 · 6,772,248 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7de7a25d9c70405cb56fb34d7c64575af95dfb8e6757894d4c09e2ccd7cd7f01

View on Chainz ↗

Height

#22,626

Difficulty

7.953755

Transactions

Size

2.21 KB

Version

Bits

07f42950

Nonce

Timestamp

7/12/2013, 5:48:05 PM

Confirmations

6,772,248

Mined by

⛏️ P2SHAS4Pf5oLcWa2Bm61YMMFth8zvCfdaGq2mN

Merkle Root

7bbb2f5ad835d9aa8e91d2d44461d45e983e305528935f966c2b891cdad13426

Transactions (2)

Coinbase90c1edbb07c579…7b9bcdc1b94452

1 in → 1 out15.8200 XPM108 B

AS4Pf5oL…fdaGq2mN

8b1b7353a6bf74…c50fcf0ef34c01

15 in → 2 out1500.0120 XPM2.01 KB

ANvmZyeW…qxiXK6QY AVya9PoB…Sxjginfx

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.

9.110 × 10⁹⁹(100-digit number)

91101751574744672839…69816112640796277999

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

9.110 × 10⁹⁹(100-digit number)

91101751574744672839…69816112640796277999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.110 × 10⁹⁹(100-digit number)

91101751574744672839…69816112640796278001

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

1.822 × 10¹⁰⁰(101-digit number)

18220350314948934567…39632225281592555999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.822 × 10¹⁰⁰(101-digit number)

18220350314948934567…39632225281592556001

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

3.644 × 10¹⁰⁰(101-digit number)

36440700629897869135…79264450563185111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.644 × 10¹⁰⁰(101-digit number)

36440700629897869135…79264450563185112001

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

7.288 × 10¹⁰⁰(101-digit number)

72881401259795738271…58528901126370223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.288 × 10¹⁰⁰(101-digit number)

72881401259795738271…58528901126370224001

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