Block #519,373

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/1/2014, 4:48:42 AM · Difficulty 10.8558 · 6,275,483 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

746090c63969a1d84284686bc79ace27b39576e3901a6d60b0efb3aa0c9a9cbb

View on Chainz ↗

Height

#519,373

Difficulty

10.855847

Transactions

Size

810 B

Version

Bits

0adb18c3

Nonce

6,683

Timestamp

5/1/2014, 4:48:42 AM

Confirmations

6,275,483

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

12f5b4fb04e45cfdf293aa0776e53b0bd73fa9765789d9941077a45d00d832ec

Transactions (3)

Coinbase656e2d53594bdc…db6c4573b81a4b

1 in → 1 out8.4900 XPM116 B

AbwWkWZt…kawDhufa

77be6d3b9d1816…4c5e622936c487

1 in → 2 out8.4800 XPM226 B

AbibgWy7…MMZXu4Bh APk9BRzn…q9iU5KgP

ff53156db609f5…40f21ff8a84407

2 in → 2 out1.0718 XPM376 B

ANGrM2P7…AGmd2gPV AbFyE8q6…fW15cPJF

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.

4.497 × 10⁹⁸(99-digit number)

44975723758102900109…39786907929072711999

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

4.497 × 10⁹⁸(99-digit number)

44975723758102900109…39786907929072711999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.497 × 10⁹⁸(99-digit number)

44975723758102900109…39786907929072712001

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

8.995 × 10⁹⁸(99-digit number)

89951447516205800219…79573815858145423999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.995 × 10⁹⁸(99-digit number)

89951447516205800219…79573815858145424001

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

1.799 × 10⁹⁹(100-digit number)

17990289503241160043…59147631716290847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.799 × 10⁹⁹(100-digit number)

17990289503241160043…59147631716290848001

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

3.598 × 10⁹⁹(100-digit number)

35980579006482320087…18295263432581695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.598 × 10⁹⁹(100-digit number)

35980579006482320087…18295263432581696001

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

7.196 × 10⁹⁹(100-digit number)

71961158012964640175…36590526865163391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.196 × 10⁹⁹(100-digit number)

71961158012964640175…36590526865163392001

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