Block #289,330

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 3:59:34 AM · Difficulty 9.9884 · 6,518,574 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dd2e77a8c4db8c1009bd737c21055c08b395c6f3397b1df8dee88c4bc17aad08

View on Chainz ↗

Height

#289,330

Difficulty

9.988431

Transactions

Size

1.08 KB

Version

Bits

09fd09d7

Nonce

59,583

Timestamp

12/2/2013, 3:59:34 AM

Confirmations

6,518,574

Mined by

⛏️ 2jaRlAc6mGvmQ9ya8dQxqWNQYGz81U4XqWmPHjR

Merkle Root

95491ddae5e29fce99b03fa1559d0512859aa0b91bb9bee151225ba8662505e7

Transactions (1)

Coinbase95491ddae5e29f…225ba8662505e7

1 in → 28 out9.9900 XPM1015 B

Ac6mGvmQ…XqWmPHjR Acs9SHrk…QJSB8SFG AXVoW9zh…1AHidHih AUQo3uDm…Dh3SMqZX AGAf8Z9Q…ggDWo52w

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.

1.683 × 10⁹²(93-digit number)

16831095616873229462…15712803847741455679

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

1.683 × 10⁹²(93-digit number)

16831095616873229462…15712803847741455679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.683 × 10⁹²(93-digit number)

16831095616873229462…15712803847741455681

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

3.366 × 10⁹²(93-digit number)

33662191233746458925…31425607695482911359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.366 × 10⁹²(93-digit number)

33662191233746458925…31425607695482911361

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

6.732 × 10⁹²(93-digit number)

67324382467492917851…62851215390965822719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.732 × 10⁹²(93-digit number)

67324382467492917851…62851215390965822721

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

1.346 × 10⁹³(94-digit number)

13464876493498583570…25702430781931645439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.346 × 10⁹³(94-digit number)

13464876493498583570…25702430781931645441

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

2.692 × 10⁹³(94-digit number)

26929752986997167140…51404861563863290879

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 #289,330

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