Block #344,264

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/5/2014, 4:58:41 AM · Difficulty 10.1910 · 6,455,103 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be3c5891e0cf2c09fc856434ad12f63b5a3f40bec47058238a39f87a1016099b

View on Chainz ↗

Height

#344,264

Difficulty

10.190959

Transactions

Size

758 B

Version

Bits

0a30e2ad

Nonce

23,331

Timestamp

1/5/2014, 4:58:41 AM

Confirmations

6,455,103

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

612b07ccd1ebe4b2abdb6bee6070efb1613adefe378b4ae747d2c51a52058b08

Transactions (2)

Coinbaseb447fb58896ec4…6f69bfd21dd9b1

1 in → 1 out9.6200 XPM110 B

AeKNrjNj…1NEq95Ta

5a1aef5f64a0f9…974b9e05792a40

3 in → 3 out1057.9766 XPM557 B

ASoVU8wk…PqSYKkyV ANAsPPYb…ncGEHyJa ARBiQ69k…HoFVx56u

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.

6.187 × 10⁹⁶(97-digit number)

61878394755470491991…76257615106327338139

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

6.187 × 10⁹⁶(97-digit number)

61878394755470491991…76257615106327338139

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.187 × 10⁹⁶(97-digit number)

61878394755470491991…76257615106327338141

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

1.237 × 10⁹⁷(98-digit number)

12375678951094098398…52515230212654676279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.237 × 10⁹⁷(98-digit number)

12375678951094098398…52515230212654676281

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

2.475 × 10⁹⁷(98-digit number)

24751357902188196796…05030460425309352559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.475 × 10⁹⁷(98-digit number)

24751357902188196796…05030460425309352561

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

4.950 × 10⁹⁷(98-digit number)

49502715804376393593…10060920850618705119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.950 × 10⁹⁷(98-digit number)

49502715804376393593…10060920850618705121

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

9.900 × 10⁹⁷(98-digit number)

99005431608752787186…20121841701237410239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.900 × 10⁹⁷(98-digit number)

99005431608752787186…20121841701237410241

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