Block #515,581

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2014, 9:14:15 PM · Difficulty 10.8418 · 6,295,521 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3e2c247df0e2bf0389d3c39c1eb428a96e8ff8023cf810a6b10ec0ee2e690d9a

View on Chainz ↗

Height

#515,581

Difficulty

10.841787

Transactions

Size

1.81 KB

Version

Bits

0ad77f54

Nonce

102,841,030

Timestamp

4/28/2014, 9:14:15 PM

Confirmations

6,295,521

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

26fec10425917b56cee202f297c6267b5f5e85fd6bb0aac28a764093266f5766

Transactions (5)

Coinbase8b8c7d5cd46c0b…2730208b274be7

1 in → 1 out8.5300 XPM116 B

AbwWkWZt…kawDhufa

16ca9928d73388…fa3111490ef3ab

5 in → 2 out68.3451 XPM821 B

AMRFEk6F…kw56GizB AWkdeMFz…8VqzqvKd

7a0f6a637ad3a0…938c47a5a7c21d

1 in → 2 out8.5000 XPM225 B

AZKkWvpr…vNwAvHqR ALzHt7oX…RZYifDqk

2422d69fe5b39d…f5e949f9ebf35a

1 in → 2 out8.5000 XPM226 B

AYyfzxw1…41CKcwF1 AXEiAGss…bZDLCVZa

2323ca43faa83a…2f713ad23a6c4f

2 in → 2 out16.5219 XPM373 B

ALSxTPyd…1PBSzfai ANGcRH5j…X8HzUSTd

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.

2.461 × 10⁹⁸(99-digit number)

24618041804756090609…73585886998951918399

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

2.461 × 10⁹⁸(99-digit number)

24618041804756090609…73585886998951918399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.461 × 10⁹⁸(99-digit number)

24618041804756090609…73585886998951918401

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

4.923 × 10⁹⁸(99-digit number)

49236083609512181218…47171773997903836799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.923 × 10⁹⁸(99-digit number)

49236083609512181218…47171773997903836801

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

9.847 × 10⁹⁸(99-digit number)

98472167219024362437…94343547995807673599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.847 × 10⁹⁸(99-digit number)

98472167219024362437…94343547995807673601

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

1.969 × 10⁹⁹(100-digit number)

19694433443804872487…88687095991615347199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.969 × 10⁹⁹(100-digit number)

19694433443804872487…88687095991615347201

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

3.938 × 10⁹⁹(100-digit number)

39388866887609744974…77374191983230694399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.938 × 10⁹⁹(100-digit number)

39388866887609744974…77374191983230694401

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

7.877 × 10⁹⁹(100-digit number)

78777733775219489949…54748383966461388799

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 #515,581

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