Block #17,095

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 12:43:06 AM · Difficulty 7.8867 · 6,797,289 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24e338015266955e13fce2bce098be92ed290c66976713bf3be14d1a8ccaad32

View on Chainz ↗

Height

#17,095

Difficulty

7.886672

Transactions

Size

3.69 KB

Version

Bits

07e2fcf7

Nonce

588

Timestamp

7/12/2013, 12:43:06 AM

Confirmations

6,797,289

Mined by

⛏️ P2SHARxrC9nN917xcrAyoaEhgBcBnKYjSAMe2d

Merkle Root

e7bb3129cb3b0db4c3cd4f1aadaefbae9c4b4ef724e63c7965bef085098f2216

Transactions (2)

Coinbase4999b71bd94e7b…e903c84b72821b

1 in → 1 out16.1000 XPM108 B

ARxrC9nN…YjSAMe2d

3f46ec63ba9b66…343ecaf9fa6f3e

30 in → 1 out458.9200 XPM3.49 KB

AVm6CvLW…GmiytmRn

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.

3.782 × 10⁹⁹(100-digit number)

37823714606694171971…85572549592353034399

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

3.782 × 10⁹⁹(100-digit number)

37823714606694171971…85572549592353034399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.782 × 10⁹⁹(100-digit number)

37823714606694171971…85572549592353034401

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

7.564 × 10⁹⁹(100-digit number)

75647429213388343942…71145099184706068799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.564 × 10⁹⁹(100-digit number)

75647429213388343942…71145099184706068801

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

1.512 × 10¹⁰⁰(101-digit number)

15129485842677668788…42290198369412137599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.512 × 10¹⁰⁰(101-digit number)

15129485842677668788…42290198369412137601

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

3.025 × 10¹⁰⁰(101-digit number)

30258971685355337576…84580396738824275199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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

Block #17,095

Cookie Preferences