Block #473,770

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 3:45:58 AM · Difficulty 10.4452 · 6,335,093 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a90c4517e236a949f81a05051399598b58587fc6f82ca7f4603a46abaee288a4

View on Chainz ↗

Height

#473,770

Difficulty

10.445166

Transactions

Size

1004 B

Version

Bits

0a71f668

Nonce

164,613

Timestamp

4/4/2014, 3:45:58 AM

Confirmations

6,335,093

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

ee280e04e6bb33d181689133f5342fe9aa57a6fd90ae584ab4ce8fa776d90f96

Transactions (1)

Coinbaseee280e04e6bb33…ce8fa776d90f96

1 in → 25 out9.1500 XPM913 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw Adbb4svj…dQWTHsq5 APtc8nU2…tp6qFHwW ASgUri65…C7NLcyBg

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.

9.546 × 10⁹⁷(98-digit number)

95461173069705670150…79079289050196526239

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

9.546 × 10⁹⁷(98-digit number)

95461173069705670150…79079289050196526239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.546 × 10⁹⁷(98-digit number)

95461173069705670150…79079289050196526241

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

1.909 × 10⁹⁸(99-digit number)

19092234613941134030…58158578100393052479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.909 × 10⁹⁸(99-digit number)

19092234613941134030…58158578100393052481

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

3.818 × 10⁹⁸(99-digit number)

38184469227882268060…16317156200786104959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.818 × 10⁹⁸(99-digit number)

38184469227882268060…16317156200786104961

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

7.636 × 10⁹⁸(99-digit number)

76368938455764536120…32634312401572209919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.636 × 10⁹⁸(99-digit number)

76368938455764536120…32634312401572209921

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

1.527 × 10⁹⁹(100-digit number)

15273787691152907224…65268624803144419839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.527 × 10⁹⁹(100-digit number)

15273787691152907224…65268624803144419841

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 #473,770

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