Block #275,010

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 12:43:35 PM · Difficulty 9.9595 · 6,520,589 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e413360b1937a4996504c681edaf61f495e211eec3ae590595b4d36575dd1609

View on Chainz ↗

Height

#275,010

Difficulty

9.959476

Transactions

Size

27.77 KB

Version

Bits

09f5a038

Nonce

387,549

Timestamp

11/26/2013, 12:43:35 PM

Confirmations

6,520,589

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e7b6fc85219f44d2b6da5dbec7c5f36e1827cfc6888333b1974b185e3c21e1e6

Transactions (3)

Coinbase616a5b6739210f…0f6f807004daeb

1 in → 1 out10.3600 XPM110 B

AeKNrjNj…1NEq95Ta

84e53459981285…ad75f38a09727f

188 in → 1 out3890.3451 XPM27.21 KB

AJg5yEcd…EdhNXGPb

a2ff1576936f20…84780671e7de72

2 in → 2 out1.0640 XPM375 B

AVyLhVCG…XQKaJq2p AcSNGDdz…EmY6jUFx

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.

1.349 × 10⁹²(93-digit number)

13492733386366618215…26031311892264990419

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

1.349 × 10⁹²(93-digit number)

13492733386366618215…26031311892264990419

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.349 × 10⁹²(93-digit number)

13492733386366618215…26031311892264990421

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

2.698 × 10⁹²(93-digit number)

26985466772733236431…52062623784529980839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.698 × 10⁹²(93-digit number)

26985466772733236431…52062623784529980841

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

5.397 × 10⁹²(93-digit number)

53970933545466472862…04125247569059961679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.397 × 10⁹²(93-digit number)

53970933545466472862…04125247569059961681

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

1.079 × 10⁹³(94-digit number)

10794186709093294572…08250495138119923359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.079 × 10⁹³(94-digit number)

10794186709093294572…08250495138119923361

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

2.158 × 10⁹³(94-digit number)

21588373418186589144…16500990276239846719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.158 × 10⁹³(94-digit number)

21588373418186589144…16500990276239846721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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