Block #289,474

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 5:28:51 AM · Difficulty 9.9886 · 6,518,730 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ff9a625123926f9494439207d4ee8343b45344415ba93c22cb98105614b16a8f

View on Chainz ↗

Height

#289,474

Difficulty

9.988561

Transactions

Size

722 B

Version

Bits

09fd1257

Nonce

76,262

Timestamp

12/2/2013, 5:28:51 AM

Confirmations

6,518,730

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

140308218c0c5534eb657312db374d33b46d6e7186bcaa3a79b5104cdc011bb6

Transactions (2)

Coinbase43629c35bcb317…b3e00e8d5b1ccb

1 in → 1 out10.0200 XPM110 B

AeKNrjNj…1NEq95Ta

82d69378592e2a…69209b1bc2e0fe

3 in → 2 out679.9130 XPM522 B

Ad9YDAvu…LEeqccGt AW6gJFKt…VkW8aDm3

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.

5.575 × 10⁹⁵(96-digit number)

55750068529704534189…65508630946420403199

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

5.575 × 10⁹⁵(96-digit number)

55750068529704534189…65508630946420403199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.575 × 10⁹⁵(96-digit number)

55750068529704534189…65508630946420403201

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

1.115 × 10⁹⁶(97-digit number)

11150013705940906837…31017261892840806399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.115 × 10⁹⁶(97-digit number)

11150013705940906837…31017261892840806401

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

2.230 × 10⁹⁶(97-digit number)

22300027411881813675…62034523785681612799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.230 × 10⁹⁶(97-digit number)

22300027411881813675…62034523785681612801

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

4.460 × 10⁹⁶(97-digit number)

44600054823763627351…24069047571363225599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.460 × 10⁹⁶(97-digit number)

44600054823763627351…24069047571363225601

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

8.920 × 10⁹⁶(97-digit number)

89200109647527254702…48138095142726451199

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 #289,474

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