Block #249,224

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/7/2013, 8:06:24 PM · Difficulty 9.9668 · 6,575,408 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

09f3dd9c862463e98339d8fb2ff3d96c0d62837bc56f27fa9ebe751698dcbc36

View on Chainz ↗

Height

#249,224

Difficulty

9.966763

Transactions

Size

423 B

Version

Bits

09f77dcf

Nonce

43,201

Timestamp

11/7/2013, 8:06:24 PM

Confirmations

6,575,408

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

9cacb602475e12d238f262393bff06cfd090674f7b855ac4ee702918c8363c94

Transactions (2)

Coinbaseb67400ac78d669…a023e5d9926bd7

1 in → 2 out10.0600 XPM142 B

AKcbk49N…GJbKa7j1 ASNt3cJa…L5zCqAYM

170984e8b7906b…51fb47145198de

1 in → 1 out98.5506 XPM192 B

ATknEwpv…tz6xvy1e

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.

6.124 × 10⁹¹(92-digit number)

61245366059688553758…42410115041924361549

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

6.124 × 10⁹¹(92-digit number)

61245366059688553758…42410115041924361549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.124 × 10⁹¹(92-digit number)

61245366059688553758…42410115041924361551

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

1.224 × 10⁹²(93-digit number)

12249073211937710751…84820230083848723099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.224 × 10⁹²(93-digit number)

12249073211937710751…84820230083848723101

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

2.449 × 10⁹²(93-digit number)

24498146423875421503…69640460167697446199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.449 × 10⁹²(93-digit number)

24498146423875421503…69640460167697446201

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

4.899 × 10⁹²(93-digit number)

48996292847750843006…39280920335394892399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.899 × 10⁹²(93-digit number)

48996292847750843006…39280920335394892401

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

9.799 × 10⁹²(93-digit number)

97992585695501686013…78561840670789784799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.799 × 10⁹²(93-digit number)

97992585695501686013…78561840670789784801

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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

Block #249,224

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