Block #223,618

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/23/2013, 3:56:33 AM · Difficulty 9.9378 · 6,568,965 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d29694d6dbb35d033c4b48763fa191e6c4b298ff6e9a5ac73f8993bac4282a95

View on Chainz ↗

Height

#223,618

Difficulty

9.937811

Transactions

Size

861 B

Version

Bits

09f01460

Nonce

61,844

Timestamp

10/23/2013, 3:56:33 AM

Confirmations

6,568,965

Merkle Root

6b348f694bb8e062fc15dfb782bfd71859de223eafa764473010b8bfed3d19ac

Transactions (5)

Coinbase7c8222f8331578…395a367c659795

1 in → 1 out10.1500 XPM109 B

AL7ySR5a…gvfBBX6X

0caca67f434d6a…83e5e342654cca

1 in → 1 out10.1600 XPM157 B

AZbnPqqW…8cDz5Rfd

4d7390e2d16ad0…d26d91686f0d29

1 in → 1 out10.1100 XPM158 B

AZbnPqqW…8cDz5Rfd

5ae49112171e63…cc8c7233417dae

1 in → 1 out10.1000 XPM158 B

AZbnPqqW…8cDz5Rfd

0304a47e6a31c5…2b9ccc51595996

1 in → 2 out10.7300 XPM191 B

AQAvQSWZ…C9mFkvux AYShykZp…LL6xRy8D

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.

1.752 × 10⁹⁰(91-digit number)

17523922432270796694…06642302604380011659

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

1.752 × 10⁹⁰(91-digit number)

17523922432270796694…06642302604380011659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.752 × 10⁹⁰(91-digit number)

17523922432270796694…06642302604380011661

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

3.504 × 10⁹⁰(91-digit number)

35047844864541593389…13284605208760023319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.504 × 10⁹⁰(91-digit number)

35047844864541593389…13284605208760023321

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

7.009 × 10⁹⁰(91-digit number)

70095689729083186778…26569210417520046639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.009 × 10⁹⁰(91-digit number)

70095689729083186778…26569210417520046641

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

1.401 × 10⁹¹(92-digit number)

14019137945816637355…53138420835040093279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.401 × 10⁹¹(92-digit number)

14019137945816637355…53138420835040093281

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

2.803 × 10⁹¹(92-digit number)

28038275891633274711…06276841670080186559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.803 × 10⁹¹(92-digit number)

28038275891633274711…06276841670080186561

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