Block #521,073

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/2/2014, 6:18:10 AM · Difficulty 10.8606 · 6,282,084 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2a0fc9bead38d259e58b60d41c8f71f7dcf62fada8b59c1070c821aabe5843f6

View on Chainz ↗

Height

#521,073

Difficulty

10.860617

Transactions

Size

24.98 KB

Version

Bits

0adc5169

Nonce

129,598,772

Timestamp

5/2/2014, 6:18:10 AM

Confirmations

6,282,084

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

90a2dca370035feacb5a94e404463a03b787cae993d12f5c7a1aad4133acf80f

Transactions (2)

Coinbasebbb5a74ebcbd01…d5671bb382ebcf

1 in → 1 out8.7200 XPM116 B

AbwWkWZt…kawDhufa

08bc15b51ada0b…273443c9dab249

171 in → 2 out500.0100 XPM24.78 KB

AJjnK9uC…VreFquR4 AKfAkvvP…2LjFguJV

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.

1.650 × 10⁹⁸(99-digit number)

16506144403905875196…98272338020204300489

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

1.650 × 10⁹⁸(99-digit number)

16506144403905875196…98272338020204300489

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.650 × 10⁹⁸(99-digit number)

16506144403905875196…98272338020204300491

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

3.301 × 10⁹⁸(99-digit number)

33012288807811750392…96544676040408600979

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.301 × 10⁹⁸(99-digit number)

33012288807811750392…96544676040408600981

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

6.602 × 10⁹⁸(99-digit number)

66024577615623500784…93089352080817201959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.602 × 10⁹⁸(99-digit number)

66024577615623500784…93089352080817201961

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

1.320 × 10⁹⁹(100-digit number)

13204915523124700156…86178704161634403919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.320 × 10⁹⁹(100-digit number)

13204915523124700156…86178704161634403921

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

2.640 × 10⁹⁹(100-digit number)

26409831046249400313…72357408323268807839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.640 × 10⁹⁹(100-digit number)

26409831046249400313…72357408323268807841

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