Block #498,159

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2014, 11:07:37 PM · Difficulty 10.7767 · 6,315,668 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f169f92b6c172a21c76bf6364a4b3f3422345ed42085e48db3f29018f0a82f71

View on Chainz ↗

Height

#498,159

Difficulty

10.776723

Transactions

Size

1.30 KB

Version

Bits

0ac6d752

Nonce

13,173,069

Timestamp

4/17/2014, 11:07:37 PM

Confirmations

6,315,668

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ca4dd446d0f8781484a27ef3434d8312ebba6f08c8276139c1d13ee01973b93d

Transactions (4)

Coinbaseedb4a2fce37bbf…7615180bbc9d71

1 in → 1 out8.6300 XPM116 B

AbwWkWZt…kawDhufa

fe72c406272a7f…6e8508629e5445

4 in → 2 out5.0180 XPM670 B

ATfGQHjT…sa5KPF3K AZoEnnQD…5GicVHBE

e680dd3f8e6207…2b8174ca7db8c2

1 in → 2 out1.1911 XPM225 B

AaUn3srK…WQn7AsHa AYCXRYPh…35mLnsfC

91aea3e2d09866…113060235a79f2

1 in → 2 out1.2244 XPM227 B

AWaxTsag…PL1cyPDP AXAVPFae…5G3oiRN5

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.

2.211 × 10⁹⁷(98-digit number)

22116275548259445729…51103804828686332679

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

2.211 × 10⁹⁷(98-digit number)

22116275548259445729…51103804828686332679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.211 × 10⁹⁷(98-digit number)

22116275548259445729…51103804828686332681

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

4.423 × 10⁹⁷(98-digit number)

44232551096518891459…02207609657372665359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.423 × 10⁹⁷(98-digit number)

44232551096518891459…02207609657372665361

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

8.846 × 10⁹⁷(98-digit number)

88465102193037782918…04415219314745330719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.846 × 10⁹⁷(98-digit number)

88465102193037782918…04415219314745330721

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

1.769 × 10⁹⁸(99-digit number)

17693020438607556583…08830438629490661439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.769 × 10⁹⁸(99-digit number)

17693020438607556583…08830438629490661441

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

3.538 × 10⁹⁸(99-digit number)

35386040877215113167…17660877258981322879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.538 × 10⁹⁸(99-digit number)

35386040877215113167…17660877258981322881

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 #498,159

Cookie Preferences