Block #73,733

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 7:31:36 AM · Difficulty 8.9950 · 6,717,685 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3ad42fb7e0e4497bbb3f044337c7996ae6a2c748b93f27cd60710399d081c3eb

View on Chainz ↗

Height

#73,733

Difficulty

8.995027

Transactions

Size

199 B

Version

Bits

08feba16

Nonce

1,180

Timestamp

7/21/2013, 7:31:36 AM

Confirmations

6,717,685

Merkle Root

5ea88255349c27f67d39fcbc5fc1e804fec02a72956d01353013ff0695de5cff

Transactions (1)

Coinbase5ea88255349c27…13ff0695de5cff

1 in → 1 out12.3400 XPM110 B

ANCYL9xh…9WyGnqDE

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.

8.764 × 10⁹¹(92-digit number)

87643817170457292477…30189328526481301439

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

8.764 × 10⁹¹(92-digit number)

87643817170457292477…30189328526481301439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.764 × 10⁹¹(92-digit number)

87643817170457292477…30189328526481301441

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

1.752 × 10⁹²(93-digit number)

17528763434091458495…60378657052962602879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.752 × 10⁹²(93-digit number)

17528763434091458495…60378657052962602881

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

3.505 × 10⁹²(93-digit number)

35057526868182916991…20757314105925205759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.505 × 10⁹²(93-digit number)

35057526868182916991…20757314105925205761

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

7.011 × 10⁹²(93-digit number)

70115053736365833982…41514628211850411519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.011 × 10⁹²(93-digit number)

70115053736365833982…41514628211850411521

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

1.402 × 10⁹³(94-digit number)

14023010747273166796…83029256423700823039

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