Block #288,573

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/1/2013, 7:41:04 PM · Difficulty 9.9878 · 6,522,290 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d2f3f333f3eb041a394ca806c4fdb3bc1110bf0b6c5ab1c3cb75a59a89881a8d

View on Chainz ↗

Height

#288,573

Difficulty

9.987798

Transactions

Size

1.11 KB

Version

Bits

09fce05a

Nonce

3,361

Timestamp

12/1/2013, 7:41:04 PM

Confirmations

6,522,290

Mined by

⛏️ =gaRCAJzWx2VDShfKP9pKK3jZqTbn4sj4ZSMit5

Merkle Root

11b76f65027f0ec32c7953a757c73373dece85358de08c70b25215653de22a34

Transactions (1)

Coinbase11b76f65027f0e…5215653de22a34

1 in → 29 out9.9900 XPM1.02 KB

AJzWx2VD…j4ZSMit5 AYcLTeXR…bscgPops Ae58nAEb…GFUA15fv AWQyM49v…zN9UeNMm AWZd1qVJ…9pj9yfPa

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.

1.368 × 10⁹²(93-digit number)

13680414045726561657…34182993792597095519

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

1.368 × 10⁹²(93-digit number)

13680414045726561657…34182993792597095519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.368 × 10⁹²(93-digit number)

13680414045726561657…34182993792597095521

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

2.736 × 10⁹²(93-digit number)

27360828091453123314…68365987585194191039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.736 × 10⁹²(93-digit number)

27360828091453123314…68365987585194191041

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

5.472 × 10⁹²(93-digit number)

54721656182906246629…36731975170388382079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.472 × 10⁹²(93-digit number)

54721656182906246629…36731975170388382081

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

1.094 × 10⁹³(94-digit number)

10944331236581249325…73463950340776764159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.094 × 10⁹³(94-digit number)

10944331236581249325…73463950340776764161

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

2.188 × 10⁹³(94-digit number)

21888662473162498651…46927900681553528319

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 #288,573

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