Block #563,105

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/26/2014, 5:29:50 PM · Difficulty 10.9648 · 6,231,035 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c4fb9f5a1d7705eb7d6e0de5e5675c7725ae40f1183eca85100502ae4ebb1730

View on Chainz ↗

Height

#563,105

Difficulty

10.964765

Transactions

Size

2.31 KB

Version

Bits

0af6fadd

Nonce

1,132,877,092

Timestamp

5/26/2014, 5:29:50 PM

Confirmations

6,231,035

Merkle Root

c2f7afbb5dc2816ec18ca699a098e738f9194ffc443f55739c04915eee3fa758

Transactions (4)

Coinbase88cb9672f6e0f0…5b2e6b136ee636

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

367cb751145069…742d9603b04f49

11 in → 2 out50.0104 XPM1.66 KB

AdWzdtYM…NUXLGd5B Ade7uJap…w6JdHYvk

d740f72b4f4e7b…a1be1a225ea5a1

1 in → 2 out3.7420 XPM226 B

APY6bU6F…oQXHVm48 AKhakwZW…Pgg7YNdu

084e2ce8a23a1c…6da80782bfa5a2

1 in → 2 out3.0180 XPM226 B

AJWeKVZp…TJGsd4VD AX7peG95…RsqMiUYv

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.

9.621 × 10⁹⁹(100-digit number)

96218726112298409978…84578456603401625599

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

9.621 × 10⁹⁹(100-digit number)

96218726112298409978…84578456603401625599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.621 × 10⁹⁹(100-digit number)

96218726112298409978…84578456603401625601

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

1.924 × 10¹⁰⁰(101-digit number)

19243745222459681995…69156913206803251199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.924 × 10¹⁰⁰(101-digit number)

19243745222459681995…69156913206803251201

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

3.848 × 10¹⁰⁰(101-digit number)

38487490444919363991…38313826413606502399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.848 × 10¹⁰⁰(101-digit number)

38487490444919363991…38313826413606502401

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

7.697 × 10¹⁰⁰(101-digit number)

76974980889838727982…76627652827213004799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.697 × 10¹⁰⁰(101-digit number)

76974980889838727982…76627652827213004801

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

1.539 × 10¹⁰¹(102-digit number)

15394996177967745596…53255305654426009599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.539 × 10¹⁰¹(102-digit number)

15394996177967745596…53255305654426009601

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