Block #500,758

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/19/2014, 8:45:50 AM · Difficulty 10.8013 · 6,308,340 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c11947bd486d74537791796df5d2cfdb0378de7508cd2b61904432c157fe2dc8

View on Chainz ↗

Height

#500,758

Difficulty

10.801282

Transactions

Size

788 B

Version

Bits

0acd20ca

Nonce

3,289,981

Timestamp

4/19/2014, 8:45:50 AM

Confirmations

6,308,340

Mined by

⛏️ P2SHAPQhYuaUfxfS1HGWdEFJrgtLUuveEbWGN3

Merkle Root

06285aa5757fed088d8366ab86ea9b0cf017c6a4f0e6a7f45c7908eb28c80f59

Transactions (2)

Coinbasefb6c7ab56c3cbc…88553a31562831

1 in → 1 out8.5700 XPM109 B

APQhYuaU…veEbWGN3

9cc8f409f4899d…d0181451c7da92

3 in → 6 out18.3025 XPM589 B

AZHEpaqf…MxbjTDc5 AbwLSonT…FZuaQsbm AKc9Rmjx…Bir3N5mm AeKNrjNj…1NEq95Ta AXqCJxua…RZtym3F2

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.

2.267 × 10⁹⁵(96-digit number)

22678643297154854165…70547994618403621399

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

2.267 × 10⁹⁵(96-digit number)

22678643297154854165…70547994618403621399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.267 × 10⁹⁵(96-digit number)

22678643297154854165…70547994618403621401

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

4.535 × 10⁹⁵(96-digit number)

45357286594309708331…41095989236807242799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.535 × 10⁹⁵(96-digit number)

45357286594309708331…41095989236807242801

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

9.071 × 10⁹⁵(96-digit number)

90714573188619416662…82191978473614485599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.071 × 10⁹⁵(96-digit number)

90714573188619416662…82191978473614485601

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

1.814 × 10⁹⁶(97-digit number)

18142914637723883332…64383956947228971199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.814 × 10⁹⁶(97-digit number)

18142914637723883332…64383956947228971201

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

3.628 × 10⁹⁶(97-digit number)

36285829275447766664…28767913894457942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.628 × 10⁹⁶(97-digit number)

36285829275447766664…28767913894457942401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

7.257 × 10⁹⁶(97-digit number)

72571658550895533329…57535827788915884799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #500,758

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