Block #498,545

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/18/2014, 4:00:40 AM · Difficulty 10.7808 · 6,299,270 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

63ff872a86dc06708807a85ea0fc94038f7da90b736425799016c15379f34a3f

View on Chainz ↗

Height

#498,545

Difficulty

10.780829

Transactions

Size

876 B

Version

Bits

0ac7e46c

Nonce

1,119,510,397

Timestamp

4/18/2014, 4:00:40 AM

Confirmations

6,299,270

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

560819c5764604872cadb0414aee7c554420ceba604337835c2a5eeb1f2477fb

Transactions (2)

Coinbase808d9fbc3857e4…6a961e978ddc93

1 in → 1 out8.6000 XPM116 B

AbwWkWZt…kawDhufa

9b3d0a4f124978…3daa81cfe11cb4

4 in → 2 out9.0299 XPM669 B

AUDDxu6r…7Dvw3z5o AcAnZQaB…3Cjt27dk

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.

5.427 × 10⁹⁷(98-digit number)

54279360727036666194…47845977281769589399

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

5.427 × 10⁹⁷(98-digit number)

54279360727036666194…47845977281769589399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.427 × 10⁹⁷(98-digit number)

54279360727036666194…47845977281769589401

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

1.085 × 10⁹⁸(99-digit number)

10855872145407333238…95691954563539178799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.085 × 10⁹⁸(99-digit number)

10855872145407333238…95691954563539178801

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

2.171 × 10⁹⁸(99-digit number)

21711744290814666477…91383909127078357599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.171 × 10⁹⁸(99-digit number)

21711744290814666477…91383909127078357601

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

4.342 × 10⁹⁸(99-digit number)

43423488581629332955…82767818254156715199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.342 × 10⁹⁸(99-digit number)

43423488581629332955…82767818254156715201

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

8.684 × 10⁹⁸(99-digit number)

86846977163258665911…65535636508313430399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.684 × 10⁹⁸(99-digit number)

86846977163258665911…65535636508313430401

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

1.736 × 10⁹⁹(100-digit number)

17369395432651733182…31071273016626860799

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