Block #281,561

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 1:51:17 AM · Difficulty 9.9773 · 6,534,584 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

76e2b4f99325f829ab476196e416d87554d8d50dcc876cff346421e22e7ace7f

View on Chainz ↗

Height

#281,561

Difficulty

9.977286

Transactions

Size

1.04 KB

Version

Bits

09fa2f65

Nonce

40,499

Timestamp

11/29/2013, 1:51:17 AM

Confirmations

6,534,584

Mined by

⛏️ KaRAGFAJ5YLhSEKHJ6SLzkv6wy6PiZEnBbk6G

Merkle Root

8a1e287368ebb9cc4987488099a3280255ebc962dc9836c20222d31732c8709f

Transactions (1)

Coinbase8a1e287368ebb9…22d31732c8709f

1 in → 27 out10.0300 XPM981 B

AGFAJ5YL…ZEnBbk6G AbtgNzNb…9Atvu81w AK3vz3dH…9NvorskL Ad9pSzHt…cpJ3y2zz APvpz12N…NjdsxTYA

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.

4.492 × 10⁸⁹(90-digit number)

44927819246368088762…59113326283624455839

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

4.492 × 10⁸⁹(90-digit number)

44927819246368088762…59113326283624455839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.492 × 10⁸⁹(90-digit number)

44927819246368088762…59113326283624455841

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

8.985 × 10⁸⁹(90-digit number)

89855638492736177525…18226652567248911679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.985 × 10⁸⁹(90-digit number)

89855638492736177525…18226652567248911681

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

1.797 × 10⁹⁰(91-digit number)

17971127698547235505…36453305134497823359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.797 × 10⁹⁰(91-digit number)

17971127698547235505…36453305134497823361

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

3.594 × 10⁹⁰(91-digit number)

35942255397094471010…72906610268995646719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.594 × 10⁹⁰(91-digit number)

35942255397094471010…72906610268995646721

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

7.188 × 10⁹⁰(91-digit number)

71884510794188942020…45813220537991293439

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 #281,561

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