Block #350,733

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 6:27:38 AM · Difficulty 10.2859 · 6,440,300 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a24c4383ba2e4151daacea988e9138b15e92eb71c9ab1ba32121905778b150fa

View on Chainz ↗

Height

#350,733

Difficulty

10.285917

Transactions

Size

412 B

Version

Bits

0a4931d9

Nonce

71,858

Timestamp

1/9/2014, 6:27:38 AM

Confirmations

6,440,300

Merkle Root

0a39e5674f9d3337261c3b8d996df98a546f52e306cd192f7a00dc1ac8349acb

Transactions (2)

Coinbase83bcb72d26e884…bc28ae9394ec74

1 in → 1 out9.4400 XPM97 B

AYCeLhqB…eqGM6KK1

81e93ff4241c93…8460c2203a5eee

1 in → 2 out3.3434 XPM226 B

AKxXt2sk…ZZmgfgbD AS2pUJat…vZvycbHg

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.

5.865 × 10⁹²(93-digit number)

58656061786696212111…02041328218250866159

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

5.865 × 10⁹²(93-digit number)

58656061786696212111…02041328218250866159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.865 × 10⁹²(93-digit number)

58656061786696212111…02041328218250866161

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

1.173 × 10⁹³(94-digit number)

11731212357339242422…04082656436501732319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.173 × 10⁹³(94-digit number)

11731212357339242422…04082656436501732321

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

2.346 × 10⁹³(94-digit number)

23462424714678484844…08165312873003464639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.346 × 10⁹³(94-digit number)

23462424714678484844…08165312873003464641

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

4.692 × 10⁹³(94-digit number)

46924849429356969689…16330625746006929279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.692 × 10⁹³(94-digit number)

46924849429356969689…16330625746006929281

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

9.384 × 10⁹³(94-digit number)

93849698858713939378…32661251492013858559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.384 × 10⁹³(94-digit number)

93849698858713939378…32661251492013858561

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