Block #282,600

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 10:54:11 AM · Difficulty 9.9794 · 6,535,372 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1498a40898ffc5ad81b2cfc721761fd2f521da3d004d84f41bbb49fb40c6d36b

View on Chainz ↗

Height

#282,600

Difficulty

9.979445

Transactions

Size

654 B

Version

Bits

09fabced

Nonce

40,283

Timestamp

11/29/2013, 10:54:11 AM

Confirmations

6,535,372

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2fd7816330961522b96e09de1f89e8802efb80d6334ee828bc83d9fa967d8758

Transactions (3)

Coinbasef41960a1c859b1…d166e2970be231

1 in → 1 out10.0500 XPM110 B

AeKNrjNj…1NEq95Ta

b43d982cb94f7b…43271a7071e7d4

1 in → 2 out3.0154 XPM226 B

AYevhLMW…v4HS3261 AVo42gW8…rBSJ3KjM

596180c3c47dee…b7f5e83b32acae

1 in → 2 out6.2871 XPM227 B

ANteyqZr…eFe71MND ANyKBgAy…kDay2aji

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.

1.275 × 10⁹⁷(98-digit number)

12752703098396849961…11728296497851299839

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

1.275 × 10⁹⁷(98-digit number)

12752703098396849961…11728296497851299839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.275 × 10⁹⁷(98-digit number)

12752703098396849961…11728296497851299841

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

2.550 × 10⁹⁷(98-digit number)

25505406196793699923…23456592995702599679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.550 × 10⁹⁷(98-digit number)

25505406196793699923…23456592995702599681

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

5.101 × 10⁹⁷(98-digit number)

51010812393587399846…46913185991405199359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.101 × 10⁹⁷(98-digit number)

51010812393587399846…46913185991405199361

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

1.020 × 10⁹⁸(99-digit number)

10202162478717479969…93826371982810398719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.020 × 10⁹⁸(99-digit number)

10202162478717479969…93826371982810398721

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

2.040 × 10⁹⁸(99-digit number)

20404324957434959938…87652743965620797439

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 #282,600

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