Block #5,897

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/10/2013, 12:03:01 AM · Difficulty 7.4135 · 6,783,671 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f819e99a8ed71764dc79af791d6b5a1e294e12f2992deeab853b4f5fb30b9f95

View on Chainz ↗

Height

#5,897

Difficulty

7.413514

Transactions

Size

204 B

Version

Bits

0769dc14

Nonce

Timestamp

7/10/2013, 12:03:01 AM

Confirmations

6,783,671

Merkle Root

9c8945c360bbd7c0b62248b379ad63b6dccdcf437c674b28be9b09c6b26a48cf

Transactions (1)

Coinbase9c8945c360bbd7…9b09c6b26a48cf

1 in → 1 out18.1700 XPM108 B

Aen8PBRb…bhERMxXC

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.

1.437 × 10¹⁰⁹(110-digit number)

14373384185056671931…58600240118851705399

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

1.437 × 10¹⁰⁹(110-digit number)

14373384185056671931…58600240118851705399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.437 × 10¹⁰⁹(110-digit number)

14373384185056671931…58600240118851705401

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

2.874 × 10¹⁰⁹(110-digit number)

28746768370113343863…17200480237703410799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.874 × 10¹⁰⁹(110-digit number)

28746768370113343863…17200480237703410801

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

5.749 × 10¹⁰⁹(110-digit number)

57493536740226687727…34400960475406821599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.749 × 10¹⁰⁹(110-digit number)

57493536740226687727…34400960475406821601

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

1.149 × 10¹¹⁰(111-digit number)

11498707348045337545…68801920950813643199

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