Block #344,678

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/5/2014, 11:01:45 AM · Difficulty 10.1989 · 6,457,807 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ca6ccbc6dccd16b0cd754c012b8c1138f1a1baf9e341ad90f98799436c53312c

View on Chainz ↗

Height

#344,678

Difficulty

10.198944

Transactions

Size

3.42 KB

Version

Bits

0a32ee01

Nonce

119,198

Timestamp

1/5/2014, 11:01:45 AM

Confirmations

6,457,807

Mined by

⛏️ P2SHAc6x3JUYEZicfK4SpqTooBNxvpbmCYciBB

Merkle Root

f04161e261be4c54d64f959166ac002e1afa00aca4fd204afbfb8512a7fa214c

Transactions (4)

Coinbased98ae1e7762778…a92693d78f17f6

1 in → 1 out9.6500 XPM109 B

Ac6x3JUY…bmCYciBB

9c88e35dafd2e9…abb48492b1c872

16 in → 2 out48.8017 XPM2.38 KB

Acvj5u8g…gL6o5obC AQmNAuN7…Gt3mUXcv

84dba93ff732f5…7a7b7a7c3ca107

1 in → 1 out9.7700 XPM157 B

AUQWNLX2…FxwsS5kV

b424b291a710ef…c143bd37ae86db

4 in → 3 out15.1715 XPM703 B

AbpDNWqV…yQGH7THk ASHs3BR3…HuFA7Lpt AJE6QDYK…j6VA8uN5

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.

1.108 × 10¹⁰¹(102-digit number)

11087975610233100521…26712750082499732479

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

1.108 × 10¹⁰¹(102-digit number)

11087975610233100521…26712750082499732479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.108 × 10¹⁰¹(102-digit number)

11087975610233100521…26712750082499732481

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

2.217 × 10¹⁰¹(102-digit number)

22175951220466201043…53425500164999464959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.217 × 10¹⁰¹(102-digit number)

22175951220466201043…53425500164999464961

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

4.435 × 10¹⁰¹(102-digit number)

44351902440932402086…06851000329998929919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.435 × 10¹⁰¹(102-digit number)

44351902440932402086…06851000329998929921

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

8.870 × 10¹⁰¹(102-digit number)

88703804881864804173…13702000659997859839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.870 × 10¹⁰¹(102-digit number)

88703804881864804173…13702000659997859841

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

1.774 × 10¹⁰²(103-digit number)

17740760976372960834…27404001319995719679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.774 × 10¹⁰²(103-digit number)

17740760976372960834…27404001319995719681

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