Block #334,749

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/29/2013, 5:16:03 PM · Difficulty 10.1599 · 6,482,237 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

79a7c8929207b4f2ca2d3f0678435904745a0c31e3e79d1fc4aaa49c815c1cef

View on Chainz ↗

Height

#334,749

Difficulty

10.159910

Transactions

Size

836 B

Version

Bits

0a28efe2

Nonce

263,216

Timestamp

12/29/2013, 5:16:03 PM

Confirmations

6,482,237

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

65ecbc0a50fd7c9bf4a45c63032f7c7acf506d8e866b7ab02f8f43a331f49c7f

Transactions (3)

Coinbasef4c33493ff3299…1728199fa7d032

1 in → 1 out9.6900 XPM110 B

AeKNrjNj…1NEq95Ta

1cfc3e9999d5b0…7b446cc746ff0e

2 in → 2 out49.0100 XPM375 B

Ad7ULYfn…Dui61Tor AdJ2RAaa…qRJTXpp7

f71f374a3c864b…3f876c5cd554e6

1 in → 3 out0.4700 XPM259 B

AX8FpNno…n1Rn34s2 AUa9EY4d…hYtiJ8JE AMrffhM2…8nvSGDws

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.

5.564 × 10⁹⁹(100-digit number)

55647909506021311851…66603985147004733759

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

5.564 × 10⁹⁹(100-digit number)

55647909506021311851…66603985147004733759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.564 × 10⁹⁹(100-digit number)

55647909506021311851…66603985147004733761

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

1.112 × 10¹⁰⁰(101-digit number)

11129581901204262370…33207970294009467519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.112 × 10¹⁰⁰(101-digit number)

11129581901204262370…33207970294009467521

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

2.225 × 10¹⁰⁰(101-digit number)

22259163802408524740…66415940588018935039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.225 × 10¹⁰⁰(101-digit number)

22259163802408524740…66415940588018935041

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

4.451 × 10¹⁰⁰(101-digit number)

44518327604817049481…32831881176037870079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.451 × 10¹⁰⁰(101-digit number)

44518327604817049481…32831881176037870081

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

8.903 × 10¹⁰⁰(101-digit number)

89036655209634098962…65663762352075740159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.903 × 10¹⁰⁰(101-digit number)

89036655209634098962…65663762352075740161

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

Block #334,749

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