Block #480,583

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/8/2014, 9:45:18 AM · Difficulty 10.5183 · 6,335,452 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7462f2317c55ec3d7eefb81f917d0995e175f71bdc445799702f23bfdb2aea1c

View on Chainz ↗

Height

#480,583

Difficulty

10.518263

Transactions

Size

935 B

Version

Bits

0a84ace3

Nonce

22,713

Timestamp

4/8/2014, 9:45:18 AM

Confirmations

6,335,452

Mined by

⛏️ GUaSC!bAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

077c5ee2ddbe7af165c5171e4788c44b29bbdc8c15283b34bc260a58622a5e58

Transactions (1)

Coinbase077c5ee2ddbe7a…260a58622a5e58

1 in → 23 out9.0200 XPM845 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1 AQ8QAT3J…rCFKuVbR AWMrD5hP…ZwsoxvZ3

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.

6.314 × 10⁹³(94-digit number)

63145957821323510080…56068596736080625919

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

6.314 × 10⁹³(94-digit number)

63145957821323510080…56068596736080625919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.314 × 10⁹³(94-digit number)

63145957821323510080…56068596736080625921

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

1.262 × 10⁹⁴(95-digit number)

12629191564264702016…12137193472161251839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.262 × 10⁹⁴(95-digit number)

12629191564264702016…12137193472161251841

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

2.525 × 10⁹⁴(95-digit number)

25258383128529404032…24274386944322503679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.525 × 10⁹⁴(95-digit number)

25258383128529404032…24274386944322503681

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

5.051 × 10⁹⁴(95-digit number)

50516766257058808064…48548773888645007359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.051 × 10⁹⁴(95-digit number)

50516766257058808064…48548773888645007361

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

1.010 × 10⁹⁵(96-digit number)

10103353251411761612…97097547777290014719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.010 × 10⁹⁵(96-digit number)

10103353251411761612…97097547777290014721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #480,583

Cookie Preferences