Block #255,807

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/11/2013, 11:26:37 AM · Difficulty 9.9747 · 6,549,940 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

00a004d2ea8a1edcc90f82540d139be7133b17c550f228e8a95c6023168622af

View on Chainz ↗

Height

#255,807

Difficulty

9.974684

Transactions

Size

493 B

Version

Bits

09f984ea

Nonce

20,125

Timestamp

11/11/2013, 11:26:37 AM

Confirmations

6,549,940

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

170f480e5ee2f7fb7f6095cf5cd12d0950d679bbb3139e5dccc1a62dad8f5c74

Transactions (2)

Coinbase7b332e958f79bf…21c60cc571a842

1 in → 2 out10.0500 XPM142 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

278c3a10f51b50…3a6d97c190ff5c

1 in → 4 out10.0300 XPM260 B

AeKNrjNj…1NEq95Ta Ab8481pR…snj7m922 AHb9D17o…rg9iXrZC AUfa5LFJ…C4BhhWGa

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.

1.095 × 10⁹⁷(98-digit number)

10956420811083555632…32083308399608571359

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

1.095 × 10⁹⁷(98-digit number)

10956420811083555632…32083308399608571359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.095 × 10⁹⁷(98-digit number)

10956420811083555632…32083308399608571361

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

2.191 × 10⁹⁷(98-digit number)

21912841622167111265…64166616799217142719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.191 × 10⁹⁷(98-digit number)

21912841622167111265…64166616799217142721

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

4.382 × 10⁹⁷(98-digit number)

43825683244334222530…28333233598434285439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.382 × 10⁹⁷(98-digit number)

43825683244334222530…28333233598434285441

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

8.765 × 10⁹⁷(98-digit number)

87651366488668445061…56666467196868570879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.765 × 10⁹⁷(98-digit number)

87651366488668445061…56666467196868570881

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

1.753 × 10⁹⁸(99-digit number)

17530273297733689012…13332934393737141759

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