Block #284,965

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 7:59:01 AM · Difficulty 9.9835 · 6,510,517 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

364b6ebdc588b6d5dd1e5af79f90dba63a64c04964c03b6da888fed29f3a65da

View on Chainz ↗

Height

#284,965

Difficulty

9.983547

Transactions

Size

1.14 KB

Version

Bits

09fbc9ba

Nonce

265,126

Timestamp

11/30/2013, 7:59:01 AM

Confirmations

6,510,517

Mined by

⛏️ %YaRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

ac89776f9ce0c7fb1573bde5c61a0d35ca2b14101dd3ee6f12e19d60b891a8c1

Transactions (1)

Coinbaseac89776f9ce0c7…e19d60b891a8c1

1 in → 30 out10.0000 XPM1.06 KB

APeshfYV…3PKcKMKH ANkX1YyE…kHwVW1hd APFsQ3Fo…xoFKrF12 AJzWx2VD…j4ZSMit5 AU3tFYHS…gK4SzeuL

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.

5.454 × 10⁹²(93-digit number)

54541634586306436591…21217581415256249119

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

5.454 × 10⁹²(93-digit number)

54541634586306436591…21217581415256249119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.454 × 10⁹²(93-digit number)

54541634586306436591…21217581415256249121

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

1.090 × 10⁹³(94-digit number)

10908326917261287318…42435162830512498239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.090 × 10⁹³(94-digit number)

10908326917261287318…42435162830512498241

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

2.181 × 10⁹³(94-digit number)

21816653834522574636…84870325661024996479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.181 × 10⁹³(94-digit number)

21816653834522574636…84870325661024996481

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

4.363 × 10⁹³(94-digit number)

43633307669045149272…69740651322049992959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.363 × 10⁹³(94-digit number)

43633307669045149272…69740651322049992961

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

8.726 × 10⁹³(94-digit number)

87266615338090298545…39481302644099985919

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