Block #476,475

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 8:49:11 PM · Difficulty 10.4728 · 6,316,360 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

87a952b4c24e8166dc571f6d857106654a3262500be9940dbd3942494c0ad5b7

View on Chainz ↗

Height

#476,475

Difficulty

10.472754

Transactions

Size

1.02 KB

Version

Bits

0a790665

Nonce

85,430

Timestamp

4/5/2014, 8:49:11 PM

Confirmations

6,316,360

Merkle Root

8c5164e9e7a0e5ef6141e78355bd67859e6b19daa7b0b255115082a895aae840

Transactions (2)

Coinbasef5e00270728f07…936572f051cd62

1 in → 1 out9.1100 XPM110 B

AeKNrjNj…1NEq95Ta

3df5506c5a7027…e03529ecf3bbbf

4 in → 10 out28.9698 XPM840 B

AM2BCdzP…oVrzbhaP AeKNrjNj…1NEq95Ta ASdRf38U…Y2hPMApF AWQhak32…eArVqMxc AQqkaF3Q…igBw1Nze

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.

1.396 × 10⁹⁷(98-digit number)

13962689488254467556…44623220335524315119

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

1.396 × 10⁹⁷(98-digit number)

13962689488254467556…44623220335524315119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.396 × 10⁹⁷(98-digit number)

13962689488254467556…44623220335524315121

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

2.792 × 10⁹⁷(98-digit number)

27925378976508935113…89246440671048630239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.792 × 10⁹⁷(98-digit number)

27925378976508935113…89246440671048630241

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

5.585 × 10⁹⁷(98-digit number)

55850757953017870226…78492881342097260479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.585 × 10⁹⁷(98-digit number)

55850757953017870226…78492881342097260481

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

1.117 × 10⁹⁸(99-digit number)

11170151590603574045…56985762684194520959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.117 × 10⁹⁸(99-digit number)

11170151590603574045…56985762684194520961

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

2.234 × 10⁹⁸(99-digit number)

22340303181207148090…13971525368389041919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.234 × 10⁹⁸(99-digit number)

22340303181207148090…13971525368389041921

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