Block #245,935

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/5/2013, 6:53:07 PM · Difficulty 9.9643 · 6,559,426 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

133abf3c247a18b5afb5bd3a8236ff686aeb044599a624b3084292e5b1deb37f

View on Chainz ↗

Height

#245,935

Difficulty

9.964278

Transactions

Size

3.13 KB

Version

Bits

09f6daec

Nonce

226,936

Timestamp

11/5/2013, 6:53:07 PM

Confirmations

6,559,426

Mined by

⛏️ Ry>;AUT1qxTxv3avbJ532uNhHh1mRst5B3qd8Z

Merkle Root

2df7faf6b31c93f223ec5118841ab8fe9aa029066d033402c9e9c60f2987c85f

Transactions (2)

Coinbase761cd4c0e60c71…3d0b7217bbd6bc

1 in → 57 out10.0400 XPM1.95 KB

AUT1qxTx…t5B3qd8Z ANuKx9Ke…wm7nrBRq Ac5sZcdP…kzV4eckG AMbCuLHZ…WSoStwkc AcEnwywz…vZtt2xTs

6ab2cf716589a5…2f9387aba5d1e4

7 in → 2 out50.3734 XPM1.09 KB

ALm4NcsA…p4NR8N6n AUiU4uvm…468FRpVA

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.

1.813 × 10⁹¹(92-digit number)

18138311466125034511…08376537978361715359

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

1.813 × 10⁹¹(92-digit number)

18138311466125034511…08376537978361715359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.813 × 10⁹¹(92-digit number)

18138311466125034511…08376537978361715361

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

3.627 × 10⁹¹(92-digit number)

36276622932250069023…16753075956723430719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.627 × 10⁹¹(92-digit number)

36276622932250069023…16753075956723430721

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

7.255 × 10⁹¹(92-digit number)

72553245864500138046…33506151913446861439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.255 × 10⁹¹(92-digit number)

72553245864500138046…33506151913446861441

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

1.451 × 10⁹²(93-digit number)

14510649172900027609…67012303826893722879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.451 × 10⁹²(93-digit number)

14510649172900027609…67012303826893722881

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

2.902 × 10⁹²(93-digit number)

29021298345800055218…34024607653787445759

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