Block #85,018

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/27/2013, 4:35:48 AM · Difficulty 9.2820 · 6,704,922 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa34e1f5e4342ceedf4a841c5ebd788d8891f0859c0c13678a5c087f46879b34

View on Chainz ↗

Height

#85,018

Difficulty

9.282006

Transactions

Size

206 B

Version

Bits

09483191

Nonce

38,933

Timestamp

7/27/2013, 4:35:48 AM

Confirmations

6,704,922

Merkle Root

aba732ffad941655b6995578305a2cb70a7c5373697aedf7a4017cadc638bf14

Transactions (1)

Coinbaseaba732ffad9416…017cadc638bf14

1 in → 1 out11.5900 XPM109 B

AK1JUKWL…oPR4rN5o

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.

1.112 × 10¹¹¹(112-digit number)

11129930740650175315…75844538463873995899

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

1.112 × 10¹¹¹(112-digit number)

11129930740650175315…75844538463873995899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.112 × 10¹¹¹(112-digit number)

11129930740650175315…75844538463873995901

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

2.225 × 10¹¹¹(112-digit number)

22259861481300350631…51689076927747991799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.225 × 10¹¹¹(112-digit number)

22259861481300350631…51689076927747991801

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

4.451 × 10¹¹¹(112-digit number)

44519722962600701262…03378153855495983599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.451 × 10¹¹¹(112-digit number)

44519722962600701262…03378153855495983601

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

8.903 × 10¹¹¹(112-digit number)

89039445925201402524…06756307710991967199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.903 × 10¹¹¹(112-digit number)

89039445925201402524…06756307710991967201

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

1.780 × 10¹¹²(113-digit number)

17807889185040280504…13512615421983934399

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