Block #339,481

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 3:40:12 AM · Difficulty 10.1259 · 6,466,374 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cceb946d1e2c56b763659ad8ea426d982409b43ee54c2b199520b993dd964c32

View on Chainz ↗

Height

#339,481

Difficulty

10.125873

Transactions

Size

1.05 KB

Version

Bits

0a203935

Nonce

430,951

Timestamp

1/2/2014, 3:40:12 AM

Confirmations

6,466,374

Mined by

⛏️ .aRUAQwRN8bEjE7sawFBq7N38V9niAV8PsTcY9

Merkle Root

0a06552357486e793e16c9520b6e448332989208ce068e630c85a6b9dcaca2d9

Transactions (1)

Coinbase0a06552357486e…85a6b9dcaca2d9

1 in → 27 out9.7400 XPM981 B

AQwRN8bE…V8PsTcY9 AYMaokrj…91i1KJLv Aac9Hjdg…P4ktypc3 AQ8QAT3J…rCFKuVbR AP5UvYhU…vLTDwkdA

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.

1.510 × 10¹⁰²(103-digit number)

15103007644078228308…16399087325753835519

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

1.510 × 10¹⁰²(103-digit number)

15103007644078228308…16399087325753835519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.510 × 10¹⁰²(103-digit number)

15103007644078228308…16399087325753835521

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

3.020 × 10¹⁰²(103-digit number)

30206015288156456616…32798174651507671039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.020 × 10¹⁰²(103-digit number)

30206015288156456616…32798174651507671041

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

6.041 × 10¹⁰²(103-digit number)

60412030576312913232…65596349303015342079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.041 × 10¹⁰²(103-digit number)

60412030576312913232…65596349303015342081

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

1.208 × 10¹⁰³(104-digit number)

12082406115262582646…31192698606030684159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.208 × 10¹⁰³(104-digit number)

12082406115262582646…31192698606030684161

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

2.416 × 10¹⁰³(104-digit number)

24164812230525165293…62385397212061368319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.416 × 10¹⁰³(104-digit number)

24164812230525165293…62385397212061368321

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