Block #339,818

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2014, 8:55:27 AM · Difficulty 10.1300 · 6,464,376 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6aaece8f9cfa151c25e59651f0b14c87d6a904e1eff99b5818073227d65d7d08

View on Chainz ↗

Height

#339,818

Difficulty

10.130043

Transactions

Size

1.74 KB

Version

Bits

0a214a86

Nonce

938,933

Timestamp

1/2/2014, 8:55:27 AM

Confirmations

6,464,376

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2c378504834f099792a231c86a5a788491af248a80214a43e22d77e61103aef1

Transactions (5)

Coinbase62f47ae422ee08…a8a0479a10ad51

1 in → 1 out9.7700 XPM110 B

AeKNrjNj…1NEq95Ta

3548f3ddf5b3fa…7f309a95e52bce

5 in → 2 out194.1313 XPM818 B

AVv8D13y…s1rCJr4M AdKUKtdc…1heybnCn

999bbcbdaf6005…d4ce5bbe2c3da7

2 in → 2 out54.6302 XPM373 B

AVv8D13y…s1rCJr4M ALsja3nC…tRMqAnPP

0c804c8cd4455e…394b445606df68

1 in → 1 out1.0900 XPM193 B

ASGVJx6m…shWMbD1i

32eb9ed2e26773…16b72eef987ed5

1 in → 1 out0.9900 XPM193 B

AcuXMHnj…K4efzXJC

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.

3.403 × 10¹⁰²(103-digit number)

34035354133210844194…88975374120974889999

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

3.403 × 10¹⁰²(103-digit number)

34035354133210844194…88975374120974889999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.403 × 10¹⁰²(103-digit number)

34035354133210844194…88975374120974890001

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

6.807 × 10¹⁰²(103-digit number)

68070708266421688389…77950748241949779999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.807 × 10¹⁰²(103-digit number)

68070708266421688389…77950748241949780001

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

1.361 × 10¹⁰³(104-digit number)

13614141653284337677…55901496483899559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.361 × 10¹⁰³(104-digit number)

13614141653284337677…55901496483899560001

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

2.722 × 10¹⁰³(104-digit number)

27228283306568675355…11802992967799119999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.722 × 10¹⁰³(104-digit number)

27228283306568675355…11802992967799120001

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

5.445 × 10¹⁰³(104-digit number)

54456566613137350711…23605985935598239999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.445 × 10¹⁰³(104-digit number)

54456566613137350711…23605985935598240001

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