Block #288,674

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 8:49:06 PM · Difficulty 9.9879 · 6,544,031 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1e02dffc90fe1199c21f5bf2386c74095202a0514775e1b05b5cffe698314b19

View on Chainz ↗

Height

#288,674

Difficulty

9.987881

Transactions

Size

901 B

Version

Bits

09fce5c8

Nonce

134,972

Timestamp

12/1/2013, 8:49:06 PM

Confirmations

6,544,031

Mined by

⛏️ gaRAYcLTeXRXcXHePDnP5p1bevW8AbscgPops

Merkle Root

fbfeee87ea108cfe3e54f5ad5a4284ebd25f89c93e104d5abdff8111d9d9c1cd

Transactions (1)

Coinbasefbfeee87ea108c…ff8111d9d9c1cd

1 in → 22 out10.0032 XPM811 B

AYcLTeXR…bscgPops Acs9SHrk…QJSB8SFG AMbCuLHZ…WSoStwkc AJj92cB9…AX3cvzBm AJAAjpaa…61jjHLEL

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.

3.099 × 10⁹⁴(95-digit number)

30998799633175300288…52616254229171170879

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

3.099 × 10⁹⁴(95-digit number)

30998799633175300288…52616254229171170879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.099 × 10⁹⁴(95-digit number)

30998799633175300288…52616254229171170881

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

6.199 × 10⁹⁴(95-digit number)

61997599266350600576…05232508458342341759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.199 × 10⁹⁴(95-digit number)

61997599266350600576…05232508458342341761

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

1.239 × 10⁹⁵(96-digit number)

12399519853270120115…10465016916684683519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.239 × 10⁹⁵(96-digit number)

12399519853270120115…10465016916684683521

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

2.479 × 10⁹⁵(96-digit number)

24799039706540240230…20930033833369367039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.479 × 10⁹⁵(96-digit number)

24799039706540240230…20930033833369367041

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

4.959 × 10⁹⁵(96-digit number)

49598079413080480460…41860067666738734079

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #288,674

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