Block #599,444

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/23/2014, 2:59:06 PM · Difficulty 10.9268 · 6,192,385 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b7c88285ad62586f2a7e161b2e23405bd1e1e4c89202ae7f136dbd230a2e058b

View on Chainz ↗

Height

#599,444

Difficulty

10.926787

Transactions

Size

810 B

Version

Bits

0aed41f2

Nonce

29,869,308

Timestamp

6/23/2014, 2:59:06 PM

Confirmations

6,192,385

Merkle Root

9be1c2dda575341f72131d38275f229622517432025dd47b9b856663ca198d64

Transactions (3)

Coinbased7037b63086f21…0363235af44c60

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

836f76dbef15ec…7f51efe006d6ed

2 in → 2 out10.5770 XPM375 B

ANXTojbJ…FWuuh6YP AFw5ADji…yZr7dDcT

bb0f90bf1557e8…43af8caf6b0c6c

1 in → 2 out2.2885 XPM227 B

AbtQvHTG…jgpNngMm AGzX6zrq…2sUqUFQZ

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.

4.389 × 10⁹⁸(99-digit number)

43893644759335204547…11849107211318613759

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

4.389 × 10⁹⁸(99-digit number)

43893644759335204547…11849107211318613759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.389 × 10⁹⁸(99-digit number)

43893644759335204547…11849107211318613761

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

8.778 × 10⁹⁸(99-digit number)

87787289518670409095…23698214422637227519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.778 × 10⁹⁸(99-digit number)

87787289518670409095…23698214422637227521

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

1.755 × 10⁹⁹(100-digit number)

17557457903734081819…47396428845274455039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.755 × 10⁹⁹(100-digit number)

17557457903734081819…47396428845274455041

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

3.511 × 10⁹⁹(100-digit number)

35114915807468163638…94792857690548910079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.511 × 10⁹⁹(100-digit number)

35114915807468163638…94792857690548910081

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

7.022 × 10⁹⁹(100-digit number)

70229831614936327276…89585715381097820159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.022 × 10⁹⁹(100-digit number)

70229831614936327276…89585715381097820161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.404 × 10¹⁰⁰(101-digit number)

14045966322987265455…79171430762195640319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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