Block #248,843

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 3:02:08 PM · Difficulty 9.9662 · 6,552,847 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8af99a542c85d43bfd9c05a6571b15cca2c4fab4a312fc99ec0b729280b6b255

View on Chainz ↗

Height

#248,843

Difficulty

9.966195

Transactions

Size

426 B

Version

Bits

09f75894

Nonce

14,331

Timestamp

11/7/2013, 3:02:08 PM

Confirmations

6,552,847

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

79c58f0418e476e1bec961c49204c70a685eed2b3684fa3044cdb225859c9c06

Transactions (2)

Coinbase72e49e79653d5e…8d392f56e84084

1 in → 2 out10.0600 XPM142 B

AKcbk49N…GJbKa7j1 AHsw4d6U…EnM8UXNZ

1643a813d9080b…b7e4f088fc3317

1 in → 2 out10.2100 XPM193 B

AQAvQSWZ…C9mFkvux AHXtUaPq…GL391bZK

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.

7.397 × 10⁹⁷(98-digit number)

73975205186755290532…30500528034384040319

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

7.397 × 10⁹⁷(98-digit number)

73975205186755290532…30500528034384040319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.397 × 10⁹⁷(98-digit number)

73975205186755290532…30500528034384040321

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

1.479 × 10⁹⁸(99-digit number)

14795041037351058106…61001056068768080639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.479 × 10⁹⁸(99-digit number)

14795041037351058106…61001056068768080641

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

2.959 × 10⁹⁸(99-digit number)

29590082074702116213…22002112137536161279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.959 × 10⁹⁸(99-digit number)

29590082074702116213…22002112137536161281

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

5.918 × 10⁹⁸(99-digit number)

59180164149404232426…44004224275072322559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.918 × 10⁹⁸(99-digit number)

59180164149404232426…44004224275072322561

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

1.183 × 10⁹⁹(100-digit number)

11836032829880846485…88008448550144645119

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