Block #518,577

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2014, 4:50:23 PM · Difficulty 10.8534 · 6,290,165 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6969a77eb01f6d40c00a01799c156a569005035bef9ce56c6703030f9ec45ec1

View on Chainz ↗

Height

#518,577

Difficulty

10.853446

Transactions

Size

584 B

Version

Bits

0ada7b6c

Nonce

133,631,724

Timestamp

4/30/2014, 4:50:23 PM

Confirmations

6,290,165

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

c55ddaf50c0a8e4cff04e9c5ae14f07c0466cb6b0a7f7e297348caff7e24b4c3

Transactions (2)

Coinbase4ffbee583f0b67…d194f4f30d750b

1 in → 1 out8.4900 XPM116 B

AbwWkWZt…kawDhufa

9ab7cefd39ada5…0d4e655a9f086e

2 in → 2 out1.1110 XPM375 B

AXnL68UR…jsxeGUhN AM9sCDB4…qQX48RF4

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.

9.391 × 10¹⁰⁰(101-digit number)

93915650425048452287…12334849735718794239

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

9.391 × 10¹⁰⁰(101-digit number)

93915650425048452287…12334849735718794239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.391 × 10¹⁰⁰(101-digit number)

93915650425048452287…12334849735718794241

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

1.878 × 10¹⁰¹(102-digit number)

18783130085009690457…24669699471437588479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.878 × 10¹⁰¹(102-digit number)

18783130085009690457…24669699471437588481

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

3.756 × 10¹⁰¹(102-digit number)

37566260170019380915…49339398942875176959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.756 × 10¹⁰¹(102-digit number)

37566260170019380915…49339398942875176961

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

7.513 × 10¹⁰¹(102-digit number)

75132520340038761830…98678797885750353919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.513 × 10¹⁰¹(102-digit number)

75132520340038761830…98678797885750353921

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

1.502 × 10¹⁰²(103-digit number)

15026504068007752366…97357595771500707839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.502 × 10¹⁰²(103-digit number)

15026504068007752366…97357595771500707841

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #518,577

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