Block #251,858

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 6:33:36 AM · Difficulty 9.9703 · 6,557,796 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3fb577da4d667cbd41e100604990d261d3d4ee1265784dddcdfa54bfb190d907

View on Chainz ↗

Height

#251,858

Difficulty

9.970343

Transactions

Size

3.49 KB

Version

Bits

09f8686a

Nonce

3,610

Timestamp

11/9/2013, 6:33:36 AM

Confirmations

6,557,796

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

c1abed45bc0992fd1940832696003285204cd27054bac6bfba6f960a36b7b22f

Transactions (5)

Coinbase46930191aef9ee…00a2a8b24e8dc1

1 in → 2 out10.1000 XPM141 B

AKcbk49N…GJbKa7j1 AKNbfPoc…jfkpwAyL

bc30d3f48f1a54…4660726a481c60

5 in → 2 out14.0200 XPM818 B

AUquEgch…KLLtEAMz AWp9cjrf…hMYdGouX

38ea8465591816…d8d8c7d0bdd56b

6 in → 2 out17.8391 XPM963 B

ATCgJfC8…EiL4E9fD AWp9cjrf…hMYdGouX

3e1ee2b819408a…6caf7964ab4231

8 in → 2 out21.3453 XPM1.23 KB

AUzGofqi…FfCXhLqm AWp9cjrf…hMYdGouX

a2c083dd5121c2…cbedfc28293506

1 in → 4 out13.9700 XPM295 B

AUjjYgWd…PSTMDT7s AW2NRZNc…Nir9uQfe AGxYGYHa…FRp3G4Gh AXjk5GEq…VBxcCVj4

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.

1.095 × 10⁹⁷(98-digit number)

10953482543738959433…64099493684771412159

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

1.095 × 10⁹⁷(98-digit number)

10953482543738959433…64099493684771412159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.095 × 10⁹⁷(98-digit number)

10953482543738959433…64099493684771412161

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

2.190 × 10⁹⁷(98-digit number)

21906965087477918866…28198987369542824319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.190 × 10⁹⁷(98-digit number)

21906965087477918866…28198987369542824321

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

4.381 × 10⁹⁷(98-digit number)

43813930174955837732…56397974739085648639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.381 × 10⁹⁷(98-digit number)

43813930174955837732…56397974739085648641

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

8.762 × 10⁹⁷(98-digit number)

87627860349911675465…12795949478171297279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.762 × 10⁹⁷(98-digit number)

87627860349911675465…12795949478171297281

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

1.752 × 10⁹⁸(99-digit number)

17525572069982335093…25591898956342594559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.752 × 10⁹⁸(99-digit number)

17525572069982335093…25591898956342594561

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 #251,858

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