Block #507,813

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/23/2014, 11:36:19 PM · Difficulty 10.8174 · 6,297,900 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fcf8f31e4eced029a23eaf76c7f46884122fd39533f79724b854712ab33bd9fe

View on Chainz ↗

Height

#507,813

Difficulty

10.817447

Transactions

Size

1.26 KB

Version

Bits

0ad14431

Nonce

39,542,814

Timestamp

4/23/2014, 11:36:19 PM

Confirmations

6,297,900

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

58092ecc8a10ecd43de078d84fd1f6394d29aa5cb8470b7157e037328d5766f9

Transactions (5)

Coinbase96598eca47972a…f3fbb2f0f55327

1 in → 1 out8.5700 XPM116 B

AbwWkWZt…kawDhufa

c4126f9bc24d8b…0f385eb29d47f7

1 in → 2 out8.5300 XPM226 B

AG8u7ddV…cU5QJSqk AeV2nt79…BwhG7L6E

8dfa15dd7386c9…ec607ac98d7181

1 in → 2 out8.5300 XPM226 B

AWPRLTpQ…TydnChD8 AXp3kPDu…BVEStUk4

05517a05d33091…02fb6788ed5be6

1 in → 2 out8.5300 XPM227 B

AW5ANXcb…S6xwru5U AMWhfZow…EH5vsb34

cf70df0740625f…3fa47a6e839bbd

2 in → 4 out9.9837 XPM407 B

Acag3ba1…JAWgJwcR AW9UAps1…PoAQ39bN ALrZxq5u…jReX3z9e AeKNrjNj…1NEq95Ta

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.

1.705 × 10⁹⁸(99-digit number)

17051837814546275276…78648491674375686219

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

1.705 × 10⁹⁸(99-digit number)

17051837814546275276…78648491674375686219

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.705 × 10⁹⁸(99-digit number)

17051837814546275276…78648491674375686221

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

3.410 × 10⁹⁸(99-digit number)

34103675629092550552…57296983348751372439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.410 × 10⁹⁸(99-digit number)

34103675629092550552…57296983348751372441

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

6.820 × 10⁹⁸(99-digit number)

68207351258185101105…14593966697502744879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.820 × 10⁹⁸(99-digit number)

68207351258185101105…14593966697502744881

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

1.364 × 10⁹⁹(100-digit number)

13641470251637020221…29187933395005489759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.364 × 10⁹⁹(100-digit number)

13641470251637020221…29187933395005489761

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

2.728 × 10⁹⁹(100-digit number)

27282940503274040442…58375866790010979519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.728 × 10⁹⁹(100-digit number)

27282940503274040442…58375866790010979521

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

5.456 × 10⁹⁹(100-digit number)

54565881006548080884…16751733580021959039

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