Block #273,878

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 12:46:21 AM · Difficulty 9.9559 · 6,567,423 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07b9b307a211d2e5c4e6ee5cceecbe72a00e394ea5b47ba0f702edeabbe67473

View on Chainz ↗

Height

#273,878

Difficulty

9.955945

Transactions

Size

17.02 KB

Version

Bits

09f4b8d3

Nonce

2,716

Timestamp

11/26/2013, 12:46:21 AM

Confirmations

6,567,423

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2a6a76c62c9494a8e9f7fe1786c4baebc3b35ffdedb4dfb1b7e02ae8004dc659

Transactions (2)

Coinbase0327d8bd6c7210…978cead2badccc

1 in → 1 out10.2600 XPM110 B

AeKNrjNj…1NEq95Ta

aca1af694be572…37819ce3146b89

116 in → 2 out17.0104 XPM16.83 KB

AeKs2KWb…iHk4NPBN AXkEVYCb…9aDaeFLp

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.

1.541 × 10⁹⁰(91-digit number)

15417999867221986265…26383069174548424799

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

1.541 × 10⁹⁰(91-digit number)

15417999867221986265…26383069174548424799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.541 × 10⁹⁰(91-digit number)

15417999867221986265…26383069174548424801

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

3.083 × 10⁹⁰(91-digit number)

30835999734443972530…52766138349096849599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.083 × 10⁹⁰(91-digit number)

30835999734443972530…52766138349096849601

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

6.167 × 10⁹⁰(91-digit number)

61671999468887945060…05532276698193699199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.167 × 10⁹⁰(91-digit number)

61671999468887945060…05532276698193699201

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

1.233 × 10⁹¹(92-digit number)

12334399893777589012…11064553396387398399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.233 × 10⁹¹(92-digit number)

12334399893777589012…11064553396387398401

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

2.466 × 10⁹¹(92-digit number)

24668799787555178024…22129106792774796799

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 #273,878

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