Block #250,400

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/8/2013, 11:48:47 AM · Difficulty 9.9683 · 6,544,184 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e476b0902ac200190d9e9a9ad52912a9cddddad91addaf1f38c8ca6266124fbf

View on Chainz ↗

Height

#250,400

Difficulty

9.968258

Transactions

Size

49.87 KB

Version

Bits

09f7dfba

Nonce

19,975

Timestamp

11/8/2013, 11:48:47 AM

Confirmations

6,544,184

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

3e37b93cabbc9e20c146c8702cdfab0a8b62d8528406ad157dfab2aff1a2316b

Transactions (4)

Coinbase4b477262faaaaf…d276e682adef78

1 in → 2 out10.5900 XPM140 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

4514273189a4e2…a9f555b82faa40

1 in → 2 out10.0500 XPM225 B

AdMxvxQ9…KTzP8E6N APovXhSy…SxuJqUMB

fe4af2b3586c93…2092e467e26a94

1 in → 2 out10.0500 XPM226 B

AXCCsfyG…SSSFr1ZK AdgY4xdL…JobmVjcP

0f80bee07a666a…e90da771d7acb3

340 in → 2 out309.0101 XPM49.20 KB

ANCGTaG4…6XJYq2tm AUDLj1yW…knQzjcRP

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.

2.522 × 10⁹⁶(97-digit number)

25229686915892004415…35109163871372374119

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

2.522 × 10⁹⁶(97-digit number)

25229686915892004415…35109163871372374119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.522 × 10⁹⁶(97-digit number)

25229686915892004415…35109163871372374121

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

5.045 × 10⁹⁶(97-digit number)

50459373831784008831…70218327742744748239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.045 × 10⁹⁶(97-digit number)

50459373831784008831…70218327742744748241

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

1.009 × 10⁹⁷(98-digit number)

10091874766356801766…40436655485489496479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.009 × 10⁹⁷(98-digit number)

10091874766356801766…40436655485489496481

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

2.018 × 10⁹⁷(98-digit number)

20183749532713603532…80873310970978992959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.018 × 10⁹⁷(98-digit number)

20183749532713603532…80873310970978992961

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

4.036 × 10⁹⁷(98-digit number)

40367499065427207065…61746621941957985919

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