Block #359,854

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 2:03:08 AM · Difficulty 10.3875 · 6,443,780 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

740b0557cf147cd584d568f5f568be8451e3e992987d588f00598a3cfebb9a0e

View on Chainz ↗

Height

#359,854

Difficulty

10.387532

Transactions

Size

1.58 KB

Version

Bits

0a633547

Nonce

376,781

Timestamp

1/15/2014, 2:03:08 AM

Confirmations

6,443,780

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

0066197731de4e9e1a0f33f6bdc183e07a10a1b23f17dc9195caf4135e187bf1

Transactions (4)

Coinbase86803ded585383…d5fcb68359bf28

1 in → 1 out9.2800 XPM110 B

AeKNrjNj…1NEq95Ta

026ef33f23bc90…a39eac8775bbe1

6 in → 2 out10.0130 XPM966 B

AKH3Kyz4…cbY9pVtN ALUb5xS7…4ZXXtV7j

e0beda767b6266…5aaa8288802ddc

1 in → 2 out5.2021 XPM227 B

AJ8mdMED…cjk2hW7u AQn9yjxk…t3Vrquof

841e0379d547eb…8ca5af8a59d73c

1 in → 2 out4.6313 XPM225 B

AK5eMZv7…7wDmjJxU AWBCbtEU…KaG5iiYU

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.

2.939 × 10⁹⁸(99-digit number)

29399085954000076836…12142506436751464719

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

2.939 × 10⁹⁸(99-digit number)

29399085954000076836…12142506436751464719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.939 × 10⁹⁸(99-digit number)

29399085954000076836…12142506436751464721

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

5.879 × 10⁹⁸(99-digit number)

58798171908000153673…24285012873502929439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.879 × 10⁹⁸(99-digit number)

58798171908000153673…24285012873502929441

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

1.175 × 10⁹⁹(100-digit number)

11759634381600030734…48570025747005858879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.175 × 10⁹⁹(100-digit number)

11759634381600030734…48570025747005858881

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

2.351 × 10⁹⁹(100-digit number)

23519268763200061469…97140051494011717759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.351 × 10⁹⁹(100-digit number)

23519268763200061469…97140051494011717761

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

4.703 × 10⁹⁹(100-digit number)

47038537526400122938…94280102988023435519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.703 × 10⁹⁹(100-digit number)

47038537526400122938…94280102988023435521

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