Block #14,035

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 3:15:40 PM · Difficulty 7.8140 · 6,792,133 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

25856a24de0605523b39d70ce51f00482b3214366f84011715a40d489a70cbb4

View on Chainz ↗

Height

#14,035

Difficulty

7.814041

Transactions

Size

197 B

Version

Bits

07d064f8

Nonce

211

Timestamp

7/11/2013, 3:15:40 PM

Confirmations

6,792,133

Mined by

⛏️ P2SHAR9WHRyzHSUDFU9ysTwMDBD47KztnGpk5W

Merkle Root

4d922d14bb43d27890cf12aba009bb4a0489b72bc401a0ed29c109f03a1c0945

Transactions (1)

Coinbase4d922d14bb43d2…c109f03a1c0945

1 in → 1 out16.3600 XPM108 B

AR9WHRyz…ztnGpk5W

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.

7.537 × 10⁹¹(92-digit number)

75376426615297246141…60672715040951737759

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

7.537 × 10⁹¹(92-digit number)

75376426615297246141…60672715040951737759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.537 × 10⁹¹(92-digit number)

75376426615297246141…60672715040951737761

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

1.507 × 10⁹²(93-digit number)

15075285323059449228…21345430081903475519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.507 × 10⁹²(93-digit number)

15075285323059449228…21345430081903475521

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

3.015 × 10⁹²(93-digit number)

30150570646118898456…42690860163806951039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.015 × 10⁹²(93-digit number)

30150570646118898456…42690860163806951041

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

6.030 × 10⁹²(93-digit number)

60301141292237796912…85381720327613902079

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