Block #302,740

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/9/2013, 11:54:35 PM · Difficulty 9.9928 · 6,493,159 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9ddaf5a2e4d2de3958f91eddb9f01eec5d651c8fe35e958fcd944ff661d6ee79

View on Chainz ↗

Height

#302,740

Difficulty

9.992798

Transactions

Size

617 B

Version

Bits

09fe2802

Nonce

89,892

Timestamp

12/9/2013, 11:54:35 PM

Confirmations

6,493,159

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

59a732c317bdf7ee7fec999034d21434ff4130853ad51212b935ad57f3daffff

Transactions (3)

Coinbase1c23c84b270e18…2806ce07d9f44a

1 in → 1 out10.0215 XPM110 B

AeKNrjNj…1NEq95Ta

db37588b0bfb5d…b1736cac6433d4

1 in → 1 out1.0000 XPM192 B

AHEUd1Ej…Dh3WzBn8

68328196a1fef9…397b01f95ba9ef

1 in → 2 out3.7498 XPM227 B

AMf7wPnV…bUfe2A8A AGfNAQTG…BNaswdDJ

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.

6.416 × 10⁸⁸(89-digit number)

64166820222304049332…36710321896907169919

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

6.416 × 10⁸⁸(89-digit number)

64166820222304049332…36710321896907169919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.416 × 10⁸⁸(89-digit number)

64166820222304049332…36710321896907169921

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

1.283 × 10⁸⁹(90-digit number)

12833364044460809866…73420643793814339839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.283 × 10⁸⁹(90-digit number)

12833364044460809866…73420643793814339841

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

2.566 × 10⁸⁹(90-digit number)

25666728088921619733…46841287587628679679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.566 × 10⁸⁹(90-digit number)

25666728088921619733…46841287587628679681

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

5.133 × 10⁸⁹(90-digit number)

51333456177843239466…93682575175257359359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.133 × 10⁸⁹(90-digit number)

51333456177843239466…93682575175257359361

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

1.026 × 10⁹⁰(91-digit number)

10266691235568647893…87365150350514718719

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