Block #161,353

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/12/2013, 2:58:54 PM · Difficulty 9.8590 · 6,635,474 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f5a29b3552273eecdad4cde562d490a1f27b9e957532e21c9ad21d47d54a6b2a

View on Chainz ↗

Height

#161,353

Difficulty

9.858962

Transactions

Size

197 B

Version

Bits

09dbe4f3

Nonce

44,189

Timestamp

9/12/2013, 2:58:54 PM

Confirmations

6,635,474

Mined by

⛏️ P2SHAYbMkPmQSCgPpQzndcP15gatjZMrnhaWgt

Merkle Root

2209e9623edd29c19907e8e740ba552d025b9f2eef7dca9207b95b68e4af855d

Transactions (1)

Coinbase2209e9623edd29…b95b68e4af855d

1 in → 1 out10.2700 XPM109 B

AYbMkPmQ…MrnhaWgt

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.

4.503 × 10⁹⁰(91-digit number)

45039650781975727187…15380749485488039519

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

4.503 × 10⁹⁰(91-digit number)

45039650781975727187…15380749485488039519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.503 × 10⁹⁰(91-digit number)

45039650781975727187…15380749485488039521

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

9.007 × 10⁹⁰(91-digit number)

90079301563951454375…30761498970976079039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.007 × 10⁹⁰(91-digit number)

90079301563951454375…30761498970976079041

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

1.801 × 10⁹¹(92-digit number)

18015860312790290875…61522997941952158079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.801 × 10⁹¹(92-digit number)

18015860312790290875…61522997941952158081

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

3.603 × 10⁹¹(92-digit number)

36031720625580581750…23045995883904316159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.603 × 10⁹¹(92-digit number)

36031720625580581750…23045995883904316161

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

7.206 × 10⁹¹(92-digit number)

72063441251161163500…46091991767808632319

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