Block #643,513

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/22/2014, 12:53:01 PM · Difficulty 10.9561 · 6,167,230 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c12f962958949efb2b1e39d93ad9720365a9a1118a331e1ffcd2a43e1d2c1ea7

View on Chainz ↗

Height

#643,513

Difficulty

10.956127

Transactions

Size

1.59 KB

Version

Bits

0af4c4bd

Nonce

261,387,758

Timestamp

7/22/2014, 12:53:01 PM

Confirmations

6,167,230

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e5729f8eea975c8e17943f81d8c6a55e1e071a90b217c995eb670d87aa387ddb

Transactions (4)

Coinbase2251869e8947ac…27c7aa6f3e6add

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

c628d84c46948b…740e93bdbf56ce

2 in → 2 out10.8118 XPM374 B

AJVMRwh1…KzH5JKMV AY5t7fjJ…QKTZR75W

8cc81e77ede05f…dde204af8a7960

5 in → 2 out10.0682 XPM817 B

Ae2KcfvC…Y5z6Ufi7 AL3J5hcH…MpdQNwbF

e627eeb0c82e26…7c39038dc7a5fd

1 in → 2 out2.9484 XPM226 B

AWeFTqSF…usRDA3NM AcYVXBoU…6fTk3b19

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.

2.760 × 10⁹⁶(97-digit number)

27601196386641292369…41948486300229118719

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

2.760 × 10⁹⁶(97-digit number)

27601196386641292369…41948486300229118719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.760 × 10⁹⁶(97-digit number)

27601196386641292369…41948486300229118721

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

5.520 × 10⁹⁶(97-digit number)

55202392773282584738…83896972600458237439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.520 × 10⁹⁶(97-digit number)

55202392773282584738…83896972600458237441

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

1.104 × 10⁹⁷(98-digit number)

11040478554656516947…67793945200916474879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.104 × 10⁹⁷(98-digit number)

11040478554656516947…67793945200916474881

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

2.208 × 10⁹⁷(98-digit number)

22080957109313033895…35587890401832949759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.208 × 10⁹⁷(98-digit number)

22080957109313033895…35587890401832949761

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

4.416 × 10⁹⁷(98-digit number)

44161914218626067791…71175780803665899519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.416 × 10⁹⁷(98-digit number)

44161914218626067791…71175780803665899521

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 #643,513

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