Block #279,274

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 7:17:28 AM · Difficulty 9.9713 · 6,530,579 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b2d0c58d3bd17b47a4668f0d85ab1d316b37975e5293946977a210f5e87d00c0

View on Chainz ↗

Height

#279,274

Difficulty

9.971256

Transactions

Size

1.11 KB

Version

Bits

09f8a437

Nonce

84,895

Timestamp

11/28/2013, 7:17:28 AM

Confirmations

6,530,579

Mined by

⛏️ BaRAFrChogVzXp457PckLuc7xAA1WPUXL5Nvj

Merkle Root

11c94fe0b782b1132610a0324353fe81bada19c6bf05e109327fa5930beef5da

Transactions (1)

Coinbase11c94fe0b782b1…7fa5930beef5da

1 in → 29 out10.0200 XPM1.02 KB

AFrChogV…PUXL5Nvj ARiyx2fi…3haoQexs AWGQhzDN…RDYvugUy ASWX42VM…XypQABkY AScAzqGc…BZ6tV1vJ

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.

1.245 × 10⁹⁴(95-digit number)

12455020489334614335…63154098354789504359

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

1.245 × 10⁹⁴(95-digit number)

12455020489334614335…63154098354789504359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.245 × 10⁹⁴(95-digit number)

12455020489334614335…63154098354789504361

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

2.491 × 10⁹⁴(95-digit number)

24910040978669228670…26308196709579008719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.491 × 10⁹⁴(95-digit number)

24910040978669228670…26308196709579008721

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

4.982 × 10⁹⁴(95-digit number)

49820081957338457340…52616393419158017439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.982 × 10⁹⁴(95-digit number)

49820081957338457340…52616393419158017441

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

9.964 × 10⁹⁴(95-digit number)

99640163914676914681…05232786838316034879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.964 × 10⁹⁴(95-digit number)

99640163914676914681…05232786838316034881

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

1.992 × 10⁹⁵(96-digit number)

19928032782935382936…10465573676632069759

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 #279,274

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