Block #1,473,029

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/26/2016, 7:21:50 PM · Difficulty 10.6927 · 5,369,181 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b75ede05b6ae94a2221f0b51307266b567ce4cfd7c281d782bad6f95fa79083e

View on Chainz ↗

Height

#1,473,029

Difficulty

10.692699

Transactions

Size

243 B

Version

Bits

0ab154b6

Nonce

232,967,231

Timestamp

2/26/2016, 7:21:50 PM

Confirmations

5,369,181

Mined by

⛏️ P2SHAdwKJkgSub5gUckyBUnSUJCm23L2zsc2ej

Merkle Root

7c218d9dca589e808e97e0818c3a00f268837726de956e1f7dbbc76cdfcf7217

Transactions (1)

Coinbase7c218d9dca589e…bbc76cdfcf7217

1 in → 2 out8.7300 XPM152 B

AdwKJkgS…L2zsc2ej ALPu3s2c…EJXLjVFh

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.

1.243 × 10⁹⁸(99-digit number)

12434008966405030235…67031315718890495999

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

1.243 × 10⁹⁸(99-digit number)

12434008966405030235…67031315718890495999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.243 × 10⁹⁸(99-digit number)

12434008966405030235…67031315718890496001

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

2.486 × 10⁹⁸(99-digit number)

24868017932810060471…34062631437780991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.486 × 10⁹⁸(99-digit number)

24868017932810060471…34062631437780992001

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

4.973 × 10⁹⁸(99-digit number)

49736035865620120943…68125262875561983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.973 × 10⁹⁸(99-digit number)

49736035865620120943…68125262875561984001

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

9.947 × 10⁹⁸(99-digit number)

99472071731240241887…36250525751123967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.947 × 10⁹⁸(99-digit number)

99472071731240241887…36250525751123968001

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

1.989 × 10⁹⁹(100-digit number)

19894414346248048377…72501051502247935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.989 × 10⁹⁹(100-digit number)

19894414346248048377…72501051502247936001

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 #1,473,029

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