Block #347,844

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/7/2014, 11:14:43 AM · Difficulty 10.2421 · 6,461,419 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ea78861b62d652605888f2f2d91c8cb2b17876e0d91f12bca776badecfdd7ddb

View on Chainz ↗

Height

#347,844

Difficulty

10.242058

Transactions

Size

1.71 KB

Version

Bits

0a3df783

Nonce

36,364

Timestamp

1/7/2014, 11:14:43 AM

Confirmations

6,461,419

Mined by

⛏️ NaRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

d2bba387b529c5392b37b480be4bfdfd46b391d941ec5b8971e80b91a058c8f8

Transactions (4)

Coinbasedd24fbe4ecb733…2239c01011ddfe

1 in → 27 out9.5200 XPM981 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 APeshfYV…3PKcKMKH AZemWJAo…6jhDtieG Ad9pSzHt…cpJ3y2zz

4d1c1c767d1aaf…f2699d288da68a

1 in → 2 out6.5742 XPM226 B

AH82fUrB…HMQA7Dya AVidrHwz…ZfDEsBfT

6980a67e847b01…455cdadcb01dac

1 in → 2 out4.3657 XPM226 B

AaurQNPX…5D1AsKGV APKydzGq…WmaAeGxX

92a188a233afd7…2b70c39e246532

1 in → 2 out2.3525 XPM226 B

AXM2Zpvp…9mdxDjwn ARoZDt7V…AwZaWPQa

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.

9.923 × 10⁹²(93-digit number)

99239080742875139277…61802703410147627519

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

9.923 × 10⁹²(93-digit number)

99239080742875139277…61802703410147627519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.923 × 10⁹²(93-digit number)

99239080742875139277…61802703410147627521

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

1.984 × 10⁹³(94-digit number)

19847816148575027855…23605406820295255039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.984 × 10⁹³(94-digit number)

19847816148575027855…23605406820295255041

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

3.969 × 10⁹³(94-digit number)

39695632297150055711…47210813640590510079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.969 × 10⁹³(94-digit number)

39695632297150055711…47210813640590510081

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

7.939 × 10⁹³(94-digit number)

79391264594300111422…94421627281181020159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.939 × 10⁹³(94-digit number)

79391264594300111422…94421627281181020161

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

1.587 × 10⁹⁴(95-digit number)

15878252918860022284…88843254562362040319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.587 × 10⁹⁴(95-digit number)

15878252918860022284…88843254562362040321

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

Block #347,844

Cookie Preferences