Block #14,589

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/11/2013, 5:04:52 PM · Difficulty 7.8298 · 6,792,394 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c58e2cfcfe8d08918f3373a8779a19083d581cdea70b087befbc810e2b3bbee

View on Chainz ↗

Height

#14,589

Difficulty

7.829765

Transactions

Size

866 B

Version

Bits

07d46b75

Nonce

439

Timestamp

7/11/2013, 5:04:52 PM

Confirmations

6,792,394

Mined by

⛏️ P2SHAM6VRLKvWNLUn43QLb3EuhPjXzByN91i1u

Merkle Root

8bdf901df672b59079f6d013aff347636a8ce64b9a2cf692c91e103c8c2fcd8b

Transactions (2)

Coinbase27f448c9b988a4…c545bd6eca2579

1 in → 1 out16.3000 XPM108 B

AM6VRLKv…ByN91i1u

0cbd9fc43d19a1…0ac01a5fe7d581

4 in → 2 out33.9788 XPM669 B

AJBjRa9Y…Tp41rxhW AJ1TQ4Qf…q9SoiDP4

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.

7.541 × 10⁹¹(92-digit number)

75414288843485348939…64515909292653512759

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

7.541 × 10⁹¹(92-digit number)

75414288843485348939…64515909292653512759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.541 × 10⁹¹(92-digit number)

75414288843485348939…64515909292653512761

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

1.508 × 10⁹²(93-digit number)

15082857768697069787…29031818585307025519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.508 × 10⁹²(93-digit number)

15082857768697069787…29031818585307025521

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

3.016 × 10⁹²(93-digit number)

30165715537394139575…58063637170614051039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.016 × 10⁹²(93-digit number)

30165715537394139575…58063637170614051041

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

6.033 × 10⁹²(93-digit number)

60331431074788279151…16127274341228102079

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 #14,589

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