Block #479,812

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 10:17:24 PM · Difficulty 10.5104 · 6,328,175 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c54e4e0d8b014c1accc53a69ad4bc4fcd2f72073e65a180a8c2c401213c4abcb

View on Chainz ↗

Height

#479,812

Difficulty

10.510376

Transactions

Size

1.76 KB

Version

Bits

0a82a7ff

Nonce

35,638

Timestamp

4/7/2014, 10:17:24 PM

Confirmations

6,328,175

Mined by

⛏️ DRLAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

0bf2869b1eef68192a3e80a698e41f5cbef97fed11b931708827943a983088f1

Transactions (2)

Coinbase9eed162a276d42…c1463040a96d32

1 in → 24 out9.0500 XPM879 B

AdFLJFhb…bsaVkAyh ASgUri65…C7NLcyBg AGz9gyZW…bo8NYQpw AdoqUYAy…tJ482T9b AQT6GR3K…nYGow82m

3d3b3498ad5f39…e0300a31542dce

4 in → 10 out30.0385 XPM838 B

AMG1smmQ…AXdTiWgv AaNiudXg…eLkWQWr4 AXDEZh15…FbrAPGkC AJtMDaUx…bUaiUT9g AP6XU4Ao…mq8mf6N9

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.

5.781 × 10⁹³(94-digit number)

57811386160428917527…08160232290027201439

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

5.781 × 10⁹³(94-digit number)

57811386160428917527…08160232290027201439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.781 × 10⁹³(94-digit number)

57811386160428917527…08160232290027201441

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

1.156 × 10⁹⁴(95-digit number)

11562277232085783505…16320464580054402879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.156 × 10⁹⁴(95-digit number)

11562277232085783505…16320464580054402881

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

2.312 × 10⁹⁴(95-digit number)

23124554464171567011…32640929160108805759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.312 × 10⁹⁴(95-digit number)

23124554464171567011…32640929160108805761

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

4.624 × 10⁹⁴(95-digit number)

46249108928343134022…65281858320217611519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.624 × 10⁹⁴(95-digit number)

46249108928343134022…65281858320217611521

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

9.249 × 10⁹⁴(95-digit number)

92498217856686268044…30563716640435223039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.249 × 10⁹⁴(95-digit number)

92498217856686268044…30563716640435223041

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 #479,812

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