Block #284,921

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/30/2013, 7:33:33 AM · Difficulty 9.9835 · 6,510,514 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0f7d367abe34a332b9619245a9094a169a2a5ac9dc68f0be63db59182a34a435

View on Chainz ↗

Height

#284,921

Difficulty

9.983482

Transactions

Size

1.18 KB

Version

Bits

09fbc57c

Nonce

38,108

Timestamp

11/30/2013, 7:33:33 AM

Confirmations

6,510,514

Mined by

⛏️ XaRUAbEG6u9h2WjTydnaF9AxFMjJz9hAXonsnG

Merkle Root

6720c74c038c3994e85852bb631ef720b60ea72630e9ecce50551886c0b0beb1

Transactions (1)

Coinbase6720c74c038c39…551886c0b0beb1

1 in → 31 out10.0000 XPM1.09 KB

AbEG6u9h…hAXonsnG Acs9SHrk…QJSB8SFG AWZd1qVJ…9pj9yfPa AGFAJ5YL…ZEnBbk6G AWQyM49v…zN9UeNMm

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.

1.140 × 10⁹²(93-digit number)

11406523802319332462…78323426740923708359

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

1.140 × 10⁹²(93-digit number)

11406523802319332462…78323426740923708359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.140 × 10⁹²(93-digit number)

11406523802319332462…78323426740923708361

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

2.281 × 10⁹²(93-digit number)

22813047604638664924…56646853481847416719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.281 × 10⁹²(93-digit number)

22813047604638664924…56646853481847416721

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

4.562 × 10⁹²(93-digit number)

45626095209277329849…13293706963694833439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.562 × 10⁹²(93-digit number)

45626095209277329849…13293706963694833441

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

9.125 × 10⁹²(93-digit number)

91252190418554659699…26587413927389666879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.125 × 10⁹²(93-digit number)

91252190418554659699…26587413927389666881

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

1.825 × 10⁹³(94-digit number)

18250438083710931939…53174827854779333759

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