Block #290,556

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 6:19:32 PM · Difficulty 9.9893 · 6,536,282 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

043744e1a72c0dc2188effe6dfe7591c92e2bc0f10adc2f23671a2c6ed0ee260

View on Chainz ↗

Height

#290,556

Difficulty

9.989284

Transactions

Size

1.14 KB

Version

Bits

09fd41b6

Nonce

198,921

Timestamp

12/2/2013, 6:19:32 PM

Confirmations

6,536,282

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

b49084e8f4e3b50cdcb1157d34e230c162728e43cb5f34c43d17906a858677b8

Transactions (2)

Coinbasea111f9d85bda22…da29282281efe9

1 in → 1 out10.0200 XPM110 B

AeKNrjNj…1NEq95Ta

ebcd851d969122…9ab1c9177e5bb4

6 in → 2 out6.2579 XPM965 B

AG7BiMtu…Qe2M6EmR AK2DjJgx…1ZwaxMpj

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.

1.085 × 10⁹⁶(97-digit number)

10854947788787139346…90246848441299118079

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

1.085 × 10⁹⁶(97-digit number)

10854947788787139346…90246848441299118079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.085 × 10⁹⁶(97-digit number)

10854947788787139346…90246848441299118081

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

2.170 × 10⁹⁶(97-digit number)

21709895577574278692…80493696882598236159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.170 × 10⁹⁶(97-digit number)

21709895577574278692…80493696882598236161

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

4.341 × 10⁹⁶(97-digit number)

43419791155148557385…60987393765196472319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.341 × 10⁹⁶(97-digit number)

43419791155148557385…60987393765196472321

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

8.683 × 10⁹⁶(97-digit number)

86839582310297114770…21974787530392944639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.683 × 10⁹⁶(97-digit number)

86839582310297114770…21974787530392944641

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

1.736 × 10⁹⁷(98-digit number)

17367916462059422954…43949575060785889279

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 #290,556

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