Block #499,517

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/18/2014, 3:58:56 PM · Difficulty 10.7916 · 6,311,414 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fcfdddec53297e15ea6587bde496fc34f54d3f3b5ec724d8667909db44ad0776

View on Chainz ↗

Height

#499,517

Difficulty

10.791571

Transactions

Size

885 B

Version

Bits

0acaa461

Nonce

334,966,761

Timestamp

4/18/2014, 3:58:56 PM

Confirmations

6,311,414

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e808448bc8267127e1a3ca6ac077fdbdce6c8ebe9f365f8f38d2e6cbb8922785

Transactions (4)

Coinbaseed66e3d8a2364d…ea3f030d7fe5f8

1 in → 1 out8.6000 XPM116 B

AbwWkWZt…kawDhufa

52c48564bc03a0…029dd7afc256af

1 in → 2 out6.5260 XPM227 B

AHhjTCPp…sb4gL8p5 AetpA1jS…Jr38R4KZ

475d095af1b1d9…0f7eab9645e046

1 in → 2 out3.5232 XPM225 B

AbF3YhvX…VHXeJyta AbHpQaD4…Giwt7ntR

f1df2c279172be…20805a99bac8f7

1 in → 2 out5.5814 XPM226 B

AGRrLX34…F9zbreRe AGiuQuAm…2W9aJX6k

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.

1.420 × 10⁹⁸(99-digit number)

14209059029788921636…41741289373475737439

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

1.420 × 10⁹⁸(99-digit number)

14209059029788921636…41741289373475737439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.420 × 10⁹⁸(99-digit number)

14209059029788921636…41741289373475737441

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

2.841 × 10⁹⁸(99-digit number)

28418118059577843273…83482578746951474879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.841 × 10⁹⁸(99-digit number)

28418118059577843273…83482578746951474881

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

5.683 × 10⁹⁸(99-digit number)

56836236119155686546…66965157493902949759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.683 × 10⁹⁸(99-digit number)

56836236119155686546…66965157493902949761

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

1.136 × 10⁹⁹(100-digit number)

11367247223831137309…33930314987805899519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.136 × 10⁹⁹(100-digit number)

11367247223831137309…33930314987805899521

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

2.273 × 10⁹⁹(100-digit number)

22734494447662274618…67860629975611799039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.273 × 10⁹⁹(100-digit number)

22734494447662274618…67860629975611799041

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 #499,517

Cookie Preferences