Block #495,166

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/16/2014, 12:32:11 PM · Difficulty 10.7317 · 6,317,298 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

60ce47d7748e987e67c654c065d7336fab48ddd70c687ccb88302d663e39dc1f

View on Chainz ↗

Height

#495,166

Difficulty

10.731661

Transactions

Size

435 B

Version

Bits

0abb4e21

Nonce

4,648,053

Timestamp

4/16/2014, 12:32:11 PM

Confirmations

6,317,298

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

f66085755f3cf41619226a8d975d4ddefea154ece632b8d0fbda3c676a0ddef0

Transactions (2)

Coinbase5f32c6bdbe1685…8ed58b6238c59f

1 in → 1 out8.6800 XPM116 B

AbwWkWZt…kawDhufa

d06c36295432f6…565f0df5c6b199

1 in → 2 out1.0768 XPM227 B

AQ236kx1…SA7ixpmc AU64TqBE…2jQo5DcT

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.

5.481 × 10⁹⁸(99-digit number)

54816262298297768687…87654688925440901119

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

5.481 × 10⁹⁸(99-digit number)

54816262298297768687…87654688925440901119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.481 × 10⁹⁸(99-digit number)

54816262298297768687…87654688925440901121

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

1.096 × 10⁹⁹(100-digit number)

10963252459659553737…75309377850881802239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.096 × 10⁹⁹(100-digit number)

10963252459659553737…75309377850881802241

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

2.192 × 10⁹⁹(100-digit number)

21926504919319107475…50618755701763604479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.192 × 10⁹⁹(100-digit number)

21926504919319107475…50618755701763604481

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

4.385 × 10⁹⁹(100-digit number)

43853009838638214950…01237511403527208959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.385 × 10⁹⁹(100-digit number)

43853009838638214950…01237511403527208961

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

8.770 × 10⁹⁹(100-digit number)

87706019677276429900…02475022807054417919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.770 × 10⁹⁹(100-digit number)

87706019677276429900…02475022807054417921

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 #495,166

Cookie Preferences