Block #201,063

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/9/2013, 9:59:58 AM · Difficulty 9.8908 · 6,595,031 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9323331c768eed0d344348722f640c756a5183761a0118ca31aa1e12dd0faa36

View on Chainz ↗

Height

#201,063

Difficulty

9.890837

Transactions

Size

4.93 KB

Version

Bits

09e40de7

Nonce

1,164,787,097

Timestamp

10/9/2013, 9:59:58 AM

Confirmations

6,595,031

Mined by

⛏️ gRUAecqcSrfqcrVDd6FdiwQxtx9vTB96kMYkX

Merkle Root

4217586b78ba9cd648728c800a9035bf21d3b086a8a29c02ea2b4334c872f51d

Transactions (1)

Coinbase4217586b78ba9c…2b4334c872f51d

1 in → 144 out10.1600 XPM4.84 KB

AecqcSrf…B96kMYkX Acyx1hwF…K4KQkWy3 AGzcqpUN…UV26KHc8 AcKcNjCB…MZipfo4V Aei2d9CH…1JreaJ9w

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.

3.703 × 10⁸⁹(90-digit number)

37038649092719740139…34061713424181876439

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

3.703 × 10⁸⁹(90-digit number)

37038649092719740139…34061713424181876439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.703 × 10⁸⁹(90-digit number)

37038649092719740139…34061713424181876441

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

7.407 × 10⁸⁹(90-digit number)

74077298185439480279…68123426848363752879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.407 × 10⁸⁹(90-digit number)

74077298185439480279…68123426848363752881

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

1.481 × 10⁹⁰(91-digit number)

14815459637087896055…36246853696727505759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.481 × 10⁹⁰(91-digit number)

14815459637087896055…36246853696727505761

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

2.963 × 10⁹⁰(91-digit number)

29630919274175792111…72493707393455011519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.963 × 10⁹⁰(91-digit number)

29630919274175792111…72493707393455011521

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

5.926 × 10⁹⁰(91-digit number)

59261838548351584223…44987414786910023039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.926 × 10⁹⁰(91-digit number)

59261838548351584223…44987414786910023041

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