Block #472,362

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2014, 5:56:53 AM · Difficulty 10.4330 · 6,343,667 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

20ae6ab398fe133b6e1f8e7e474040d1d978868721c78c3e50691c24e9f07860

View on Chainz ↗

Height

#472,362

Difficulty

10.433043

Transactions

Size

2.06 KB

Version

Bits

0a6edbe0

Nonce

159,344

Timestamp

4/3/2014, 5:56:53 AM

Confirmations

6,343,667

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

6bc8d35ed71c2f39859ec990d143cb67cfb31d584945c5b644925e390e18b66f

Transactions (2)

Coinbase4d3766355dc95d…faafee1f449217

1 in → 3 out9.1900 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

83b4f8679dae8f…b9cfad01ae4428

9 in → 23 out74.8621 XPM1.81 KB

AJi3hMaK…QeUAXxiv AKenziQA…jfhjbJcR AHLyZUb7…cHnQjZJ9 AMUH1Z1t…Q1XW99zU AUKY4iAt…WDGQgDvd

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.

3.917 × 10⁹⁴(95-digit number)

39178270423328282669…97416813339852792799

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

3.917 × 10⁹⁴(95-digit number)

39178270423328282669…97416813339852792799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.917 × 10⁹⁴(95-digit number)

39178270423328282669…97416813339852792801

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

7.835 × 10⁹⁴(95-digit number)

78356540846656565339…94833626679705585599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.835 × 10⁹⁴(95-digit number)

78356540846656565339…94833626679705585601

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

1.567 × 10⁹⁵(96-digit number)

15671308169331313067…89667253359411171199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.567 × 10⁹⁵(96-digit number)

15671308169331313067…89667253359411171201

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

3.134 × 10⁹⁵(96-digit number)

31342616338662626135…79334506718822342399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.134 × 10⁹⁵(96-digit number)

31342616338662626135…79334506718822342401

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

6.268 × 10⁹⁵(96-digit number)

62685232677325252271…58669013437644684799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.268 × 10⁹⁵(96-digit number)

62685232677325252271…58669013437644684801

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 #472,362

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