Block #284,673

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 5:15:30 AM · Difficulty 9.9831 · 6,546,373 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

075b44446964444e357967b46e1d485a1fd3a4531ee5dfcdc035f62b44fa0bc8

View on Chainz ↗

Height

#284,673

Difficulty

9.983111

Transactions

Size

1.01 KB

Version

Bits

09fbad23

Nonce

1,138

Timestamp

11/30/2013, 5:15:30 AM

Confirmations

6,546,373

Mined by

⛏️ XaRtmoAT5YHFNEpS2kQq4oz9fUrmQVccwEB3sX3V

Merkle Root

90d99928693eec20f71bd4709da648fa01ba4ce656430299ab3b73bffc15c80a

Transactions (1)

Coinbase90d99928693eec…3b73bffc15c80a

1 in → 26 out10.0200 XPM947 B

AT5YHFNE…wEB3sX3V AcV6Mfwh…VmSjCD4e AU3PaCwF…92DCmeEV AbtgNzNb…9Atvu81w AeTzrsyg…pyKiRaaj

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.

2.309 × 10⁹⁸(99-digit number)

23095188207508985454…89070457401282162649

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

2.309 × 10⁹⁸(99-digit number)

23095188207508985454…89070457401282162649

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.309 × 10⁹⁸(99-digit number)

23095188207508985454…89070457401282162651

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

4.619 × 10⁹⁸(99-digit number)

46190376415017970908…78140914802564325299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.619 × 10⁹⁸(99-digit number)

46190376415017970908…78140914802564325301

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

9.238 × 10⁹⁸(99-digit number)

92380752830035941816…56281829605128650599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.238 × 10⁹⁸(99-digit number)

92380752830035941816…56281829605128650601

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

1.847 × 10⁹⁹(100-digit number)

18476150566007188363…12563659210257301199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.847 × 10⁹⁹(100-digit number)

18476150566007188363…12563659210257301201

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

3.695 × 10⁹⁹(100-digit number)

36952301132014376726…25127318420514602399

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 #284,673

Cookie Preferences