Block #2,178,542

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/26/2017, 4:12:17 AM · Difficulty 10.9265 · 4,659,015 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9f9abd2920a68af09f5b0353149906e6e9591bdc4fe7db4cfa79d39adbbb5ed0

View on Chainz ↗

Height

#2,178,542

Difficulty

10.926467

Transactions

Size

427 B

Version

Bits

0aed2ce9

Nonce

730,634,143

Timestamp

6/26/2017, 4:12:17 AM

Confirmations

4,659,015

Mined by

⛏️ P2SHAVJXTvibsxDnLozJqH6ZvPjSoyaUxVtWuo

Merkle Root

4220eb8c342244e4a1b31dd9c419ccfceef48abe0a0ce996798b561ff762b14d

Transactions (2)

Coinbase004c664c490e6f…7f41516884c0ea

1 in → 1 out8.3700 XPM110 B

AVJXTvib…aUxVtWuo

e482c40b479f1d…87211b45d8643c

1 in → 2 out93113.8653 XPM226 B

AGch1BwS…2izGfXD8 ALH9ZGvf…fmXRFAVF

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.

3.738 × 10⁹⁶(97-digit number)

37389310605736603152…46627425962939775999

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

3.738 × 10⁹⁶(97-digit number)

37389310605736603152…46627425962939775999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.738 × 10⁹⁶(97-digit number)

37389310605736603152…46627425962939776001

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

7.477 × 10⁹⁶(97-digit number)

74778621211473206304…93254851925879551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.477 × 10⁹⁶(97-digit number)

74778621211473206304…93254851925879552001

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

1.495 × 10⁹⁷(98-digit number)

14955724242294641260…86509703851759103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.495 × 10⁹⁷(98-digit number)

14955724242294641260…86509703851759104001

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

2.991 × 10⁹⁷(98-digit number)

29911448484589282521…73019407703518207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.991 × 10⁹⁷(98-digit number)

29911448484589282521…73019407703518208001

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

5.982 × 10⁹⁷(98-digit number)

59822896969178565043…46038815407036415999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.982 × 10⁹⁷(98-digit number)

59822896969178565043…46038815407036416001

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 #2,178,542

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