Block #252,725

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/9/2013, 5:53:35 PM · Difficulty 9.9714 · 6,542,635 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c0f93f7c197d5385393d987f966bd6c28254bd7a0886fdb08ad3f69de3395319

View on Chainz ↗

Height

#252,725

Difficulty

9.971447

Transactions

Size

1.04 KB

Version

Bits

09f8b0c1

Nonce

14,642

Timestamp

11/9/2013, 5:53:35 PM

Confirmations

6,542,635

Mined by

⛏️ P2SHAKcbk49N7DP3nse7MJr3Ed6rZiGJbKa7j1

Merkle Root

bc8154f65c913b06e975a69c0e2d9d87dddc922111753447a2851f05e031b9d0

Transactions (4)

Coinbaseb8342f333a3b6d…6a61e23165fc44

1 in → 2 out10.0700 XPM142 B

AKcbk49N…GJbKa7j1 ALfEGCwh…VawujfMm

332812e58b2c81…f75a064702848e

2 in → 2 out260.0210 XPM376 B

AZkWbWEe…5KkiDMds Aax1hUHD…6k9LuXov

8e99f2ce7ea6f5…54646bf8e279d1

1 in → 2 out4.9980 XPM226 B

AQZw8Qi1…mC2jeGbR AWBkqPMM…QnvK8aGb

f54fc04b265a70…404e3bac1d44c4

1 in → 2 out5.9247 XPM226 B

Ab3eEgKK…8WswiTix AQAwXriJ…UHZbfTWn

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.

4.794 × 10⁹⁵(96-digit number)

47941665105880215113…62270900694441020959

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

4.794 × 10⁹⁵(96-digit number)

47941665105880215113…62270900694441020959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.794 × 10⁹⁵(96-digit number)

47941665105880215113…62270900694441020961

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

9.588 × 10⁹⁵(96-digit number)

95883330211760430227…24541801388882041919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.588 × 10⁹⁵(96-digit number)

95883330211760430227…24541801388882041921

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

1.917 × 10⁹⁶(97-digit number)

19176666042352086045…49083602777764083839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.917 × 10⁹⁶(97-digit number)

19176666042352086045…49083602777764083841

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

3.835 × 10⁹⁶(97-digit number)

38353332084704172090…98167205555528167679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.835 × 10⁹⁶(97-digit number)

38353332084704172090…98167205555528167681

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

7.670 × 10⁹⁶(97-digit number)

76706664169408344181…96334411111056335359

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