Block #201,140

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/9/2013, 11:12:46 AM · Difficulty 9.8909 · 6,595,120 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e2445b3f06a6599735996910c8defb0f28ee0062a182fa1f09739d741472bdcd

View on Chainz ↗

Height

#201,140

Difficulty

9.890880

Transactions

Size

423 B

Version

Bits

09e410b0

Nonce

28,029

Timestamp

10/9/2013, 11:12:46 AM

Confirmations

6,595,120

Mined by

⛏️ P2SHASeXJJsTuk2nKV74JiRd8kaBoaFfTkAVgb

Merkle Root

ba6166b4735a58c06b66f210ad0150a9d92183a46785b82144f8ae9b8fc7330c

Transactions (2)

Coinbase9d6cc419497f96…099288bf62ee2a

1 in → 1 out10.2200 XPM109 B

ASeXJJsT…FfTkAVgb

b5a05f892200e0…20f810f1d34e7e

1 in → 2 out10.2100 XPM226 B

AYyo3srA…VwLQeJPR AV91Z8qS…e9p4tgyu

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.

1.872 × 10⁸⁹(90-digit number)

18725800067779485522…18687022471236345159

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

1.872 × 10⁸⁹(90-digit number)

18725800067779485522…18687022471236345159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.872 × 10⁸⁹(90-digit number)

18725800067779485522…18687022471236345161

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

3.745 × 10⁸⁹(90-digit number)

37451600135558971045…37374044942472690319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.745 × 10⁸⁹(90-digit number)

37451600135558971045…37374044942472690321

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

7.490 × 10⁸⁹(90-digit number)

74903200271117942091…74748089884945380639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.490 × 10⁸⁹(90-digit number)

74903200271117942091…74748089884945380641

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

1.498 × 10⁹⁰(91-digit number)

14980640054223588418…49496179769890761279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.498 × 10⁹⁰(91-digit number)

14980640054223588418…49496179769890761281

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

2.996 × 10⁹⁰(91-digit number)

29961280108447176836…98992359539781522559

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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