Block #284,429

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 3:12:27 AM · Difficulty 9.9827 · 6,510,269 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3123e6dbff3c755683177588946c82e85d184c43afc48de54043cc88031796f0

View on Chainz ↗

Height

#284,429

Difficulty

9.982691

Transactions

Size

1013 B

Version

Bits

09fb919b

Nonce

4,632

Timestamp

11/30/2013, 3:12:27 AM

Confirmations

6,510,269

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

4808f11fc5c69cee93dee088d4730b9edfe7320dc7cad6f813070b049aa4111a

Transactions (2)

Coinbase0b89a24f5cd174…8bbe8f1765c05d

1 in → 2 out10.0300 XPM141 B

AYaTpnoD…EJq25nUy ASNt3cJa…L5zCqAYM

92d7bba2a338e5…3bdc866d2601ce

5 in → 1 out1.6027 XPM781 B

AHJVDVQm…UAZtzbcw

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.

1.188 × 10⁹⁶(97-digit number)

11888822466682049107…88122212749486592639

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

1.188 × 10⁹⁶(97-digit number)

11888822466682049107…88122212749486592639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.188 × 10⁹⁶(97-digit number)

11888822466682049107…88122212749486592641

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

2.377 × 10⁹⁶(97-digit number)

23777644933364098214…76244425498973185279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.377 × 10⁹⁶(97-digit number)

23777644933364098214…76244425498973185281

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

4.755 × 10⁹⁶(97-digit number)

47555289866728196428…52488850997946370559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.755 × 10⁹⁶(97-digit number)

47555289866728196428…52488850997946370561

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

9.511 × 10⁹⁶(97-digit number)

95110579733456392856…04977701995892741119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.511 × 10⁹⁶(97-digit number)

95110579733456392856…04977701995892741121

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

1.902 × 10⁹⁷(98-digit number)

19022115946691278571…09955403991785482239

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