Block #329,414

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/25/2013, 10:56:23 PM · Difficulty 10.1718 · 6,464,004 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

816349f8246478d26be1eedb4dcaa07f8c8a753cbe6214ca2ea5ce6256805346

View on Chainz ↗

Height

#329,414

Difficulty

10.171754

Transactions

Size

1.28 KB

Version

Bits

0a2bf811

Nonce

325,323

Timestamp

12/25/2013, 10:56:23 PM

Confirmations

6,464,004

Merkle Root

36f06311001f7439c26a8d75c2f738ab7bcca6dfbd19058683a513117944c4a0

Transactions (3)

Coinbase7973fc74372774…3c8676d7a53388

1 in → 1 out9.6800 XPM110 B

AeKNrjNj…1NEq95Ta

f4ef192a78f104…eed1d7668ca9b5

4 in → 13 out38.4600 XPM908 B

AXtfS5C1…E4nEAZxW AVeKgkNY…ojVwug7M ASHs3BR3…HuFA7Lpt Ad15gKfJ…iZMkZt6b ARxZwSxP…48ZKixP1

28fd51b31c69ac…1eebe6da76a243

1 in → 1 out0.0300 XPM191 B

AQpeucYE…g3iNZEen

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.

2.217 × 10¹¹¹(112-digit number)

22175693162085794594…95714817136319733759

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

2.217 × 10¹¹¹(112-digit number)

22175693162085794594…95714817136319733759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.217 × 10¹¹¹(112-digit number)

22175693162085794594…95714817136319733761

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

4.435 × 10¹¹¹(112-digit number)

44351386324171589189…91429634272639467519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.435 × 10¹¹¹(112-digit number)

44351386324171589189…91429634272639467521

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

8.870 × 10¹¹¹(112-digit number)

88702772648343178379…82859268545278935039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.870 × 10¹¹¹(112-digit number)

88702772648343178379…82859268545278935041

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

1.774 × 10¹¹²(113-digit number)

17740554529668635675…65718537090557870079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.774 × 10¹¹²(113-digit number)

17740554529668635675…65718537090557870081

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

3.548 × 10¹¹²(113-digit number)

35481109059337271351…31437074181115740159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.548 × 10¹¹²(113-digit number)

35481109059337271351…31437074181115740161

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