Block #81,835

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/25/2013, 12:53:53 AM · Difficulty 9.2703 · 6,713,041 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

22d90380a57cee06ba38049e215c17252b7d736a428b5f0b3975a47a1944b3fd

View on Chainz ↗

Height

#81,835

Difficulty

9.270308

Transactions

Size

742 B

Version

Bits

094532e9

Nonce

Timestamp

7/25/2013, 12:53:53 AM

Confirmations

6,713,041

Mined by

⛏️ P2SHAL5jK8EfwJTaQ6XgQfgK6rhy5FnyWxdw5q

Merkle Root

cbe27a5ea60d63deb189ac10d41b2780fa102713da9ebb11994f62b2904a6b62

Transactions (2)

Coinbase2d88e0940f6da9…81f6c8807b043b

1 in → 1 out11.6300 XPM110 B

AL5jK8Ef…nyWxdw5q

a07ead31266362…57dd69fa75bdb1

4 in → 2 out69.4200 XPM534 B

AGLmMF8Y…8nXqyr8H AeJbypM3…vrboebN9

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.

5.597 × 10¹¹⁴(115-digit number)

55979480242632791113…23398909449261427279

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

5.597 × 10¹¹⁴(115-digit number)

55979480242632791113…23398909449261427279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.597 × 10¹¹⁴(115-digit number)

55979480242632791113…23398909449261427281

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

1.119 × 10¹¹⁵(116-digit number)

11195896048526558222…46797818898522854559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.119 × 10¹¹⁵(116-digit number)

11195896048526558222…46797818898522854561

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

2.239 × 10¹¹⁵(116-digit number)

22391792097053116445…93595637797045709119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.239 × 10¹¹⁵(116-digit number)

22391792097053116445…93595637797045709121

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

4.478 × 10¹¹⁵(116-digit number)

44783584194106232891…87191275594091418239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.478 × 10¹¹⁵(116-digit number)

44783584194106232891…87191275594091418241

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

8.956 × 10¹¹⁵(116-digit number)

89567168388212465782…74382551188182836479

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