Block #221,433

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/21/2013, 2:03:39 PM · Difficulty 9.9388 · 6,584,357 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0cebfada438c25b4667911c9ed382efa494e86cb4cf86fdac1dd4413f98d0e9

View on Chainz ↗

Height

#221,433

Difficulty

9.938833

Transactions

Size

787 B

Version

Bits

09f0575c

Nonce

24,267

Timestamp

10/21/2013, 2:03:39 PM

Confirmations

6,584,357

Mined by

⛏️ P2SHATbN2fgLeubaT3jjKLjxhXWqE5mY2ZknMy

Merkle Root

1bc878bf7c67ac45af711b646e99ced9472e9d07281b4006c75ed6a9ba79c95a

Transactions (2)

Coinbaseb1e92609f669e5…5abc847bf29eec

1 in → 1 out10.1200 XPM109 B

ATbN2fgL…mY2ZknMy

3a5949394e509b…e3781549ce3c9a

3 in → 5 out13.3227 XPM590 B

AeSuQFd1…8d7bTNeZ AShZWWvs…ev6wVf2R Acs9SHrk…QJSB8SFG AbuU1HhS…JPwsJEbB AHLyZUb7…cHnQjZJ9

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.

2.273 × 10⁹⁰(91-digit number)

22736928297520030791…68649618567148911159

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

2.273 × 10⁹⁰(91-digit number)

22736928297520030791…68649618567148911159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.273 × 10⁹⁰(91-digit number)

22736928297520030791…68649618567148911161

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

4.547 × 10⁹⁰(91-digit number)

45473856595040061583…37299237134297822319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.547 × 10⁹⁰(91-digit number)

45473856595040061583…37299237134297822321

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

9.094 × 10⁹⁰(91-digit number)

90947713190080123167…74598474268595644639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.094 × 10⁹⁰(91-digit number)

90947713190080123167…74598474268595644641

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

1.818 × 10⁹¹(92-digit number)

18189542638016024633…49196948537191289279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.818 × 10⁹¹(92-digit number)

18189542638016024633…49196948537191289281

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

3.637 × 10⁹¹(92-digit number)

36379085276032049266…98393897074382578559

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