Block #498,964

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/18/2014, 8:52:07 AM · Difficulty 10.7863 · 6,309,339 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ff7726f111382b9e17bd575f918199983a9463781188a45d82bfb49ea2224e84

View on Chainz ↗

Height

#498,964

Difficulty

10.786290

Transactions

Size

478 B

Version

Bits

0ac94a47

Nonce

854,253,455

Timestamp

4/18/2014, 8:52:07 AM

Confirmations

6,309,339

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

fd598668b8e32b1f2a7e715cde8b94aa75e99236a49913c9985724fcb8fb7af3

Transactions (2)

Coinbase7a7b64bc084a0d…6e5f07439a45d0

1 in → 1 out8.5900 XPM116 B

AbwWkWZt…kawDhufa

188f29ba959c5c…ee111867bac4b2

2 in → 1 out18.2237 XPM271 B

AXamPAZD…v2PLtpVh

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.

1.990 × 10⁹⁷(98-digit number)

19903525757986145759…27180691781546374739

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

1.990 × 10⁹⁷(98-digit number)

19903525757986145759…27180691781546374739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.990 × 10⁹⁷(98-digit number)

19903525757986145759…27180691781546374741

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

3.980 × 10⁹⁷(98-digit number)

39807051515972291518…54361383563092749479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.980 × 10⁹⁷(98-digit number)

39807051515972291518…54361383563092749481

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

7.961 × 10⁹⁷(98-digit number)

79614103031944583036…08722767126185498959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.961 × 10⁹⁷(98-digit number)

79614103031944583036…08722767126185498961

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

1.592 × 10⁹⁸(99-digit number)

15922820606388916607…17445534252370997919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.592 × 10⁹⁸(99-digit number)

15922820606388916607…17445534252370997921

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

3.184 × 10⁹⁸(99-digit number)

31845641212777833214…34891068504741995839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.184 × 10⁹⁸(99-digit number)

31845641212777833214…34891068504741995841

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 #498,964

Cookie Preferences