Block #511,980

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/26/2014, 2:19:50 PM · Difficulty 10.8315 · 6,295,488 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4dac50abd6676f1fe83d3830913cacf944258872315915ee5e0dd02a3406eac8

View on Chainz ↗

Height

#511,980

Difficulty

10.831523

Transactions

Size

16.05 KB

Version

Bits

0ad4deab

Nonce

369,052,042

Timestamp

4/26/2014, 2:19:50 PM

Confirmations

6,295,488

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

54a284ddfc9bade626507a54794c9ee72ac2cf7fedf3b5da14b14cc74d9eaec3

Transactions (3)

Coinbased6e74292a829aa…621978c5b33ce7

1 in → 1 out8.6800 XPM116 B

AbwWkWZt…kawDhufa

f80768e7d0d9c8…4fb7a545617be8

2 in → 1 out16.2160 XPM307 B

AaqK9b8G…R9SQWqLr

8116120c43fa32…9b800e708d5084

107 in → 2 out34.0901 XPM15.55 KB

APScje28…mkEoY3Ue AP1eWgqP…VhRVHDy4

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.

3.097 × 10⁹⁸(99-digit number)

30974769804665718832…34626324189036288639

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

3.097 × 10⁹⁸(99-digit number)

30974769804665718832…34626324189036288639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.097 × 10⁹⁸(99-digit number)

30974769804665718832…34626324189036288641

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

6.194 × 10⁹⁸(99-digit number)

61949539609331437665…69252648378072577279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.194 × 10⁹⁸(99-digit number)

61949539609331437665…69252648378072577281

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

1.238 × 10⁹⁹(100-digit number)

12389907921866287533…38505296756145154559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.238 × 10⁹⁹(100-digit number)

12389907921866287533…38505296756145154561

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

2.477 × 10⁹⁹(100-digit number)

24779815843732575066…77010593512290309119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.477 × 10⁹⁹(100-digit number)

24779815843732575066…77010593512290309121

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

4.955 × 10⁹⁹(100-digit number)

49559631687465150132…54021187024580618239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.955 × 10⁹⁹(100-digit number)

49559631687465150132…54021187024580618241

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 #511,980

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