Block #1,542,026

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/15/2016, 5:29:37 AM · Difficulty 10.6481 · 5,283,010 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b276b6d3f14b386303dafbc8a3c967e7e7e5e4333fc85048abc0372666493d27

View on Chainz ↗

Height

#1,542,026

Difficulty

10.648087

Transactions

Size

3.30 KB

Version

Bits

0aa5e908

Nonce

1,790,621,294

Timestamp

4/15/2016, 5:29:37 AM

Confirmations

5,283,010

Mined by

⛏️ P2SHAGHrFacxkrmJchGUXKD1gmgRaDAkFNcab4

Merkle Root

020042f6715b60e2e8427eda3c8463d15b97233603f27cc6c7cdce535529c8f3

Transactions (2)

Coinbase2a811de02c2813…fd13e05d27f8d8

1 in → 1 out8.8500 XPM109 B

AGHrFacx…AkFNcab4

924629d7ef40ae…2049e891457039

21 in → 2 out168.8565 XPM3.11 KB

AWF4rtPp…LnbQHVaN ALyRMTJV…p6WhyFWe

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.

5.249 × 10⁹⁴(95-digit number)

52497260872527102079…32763647608097318999

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

5.249 × 10⁹⁴(95-digit number)

52497260872527102079…32763647608097318999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.249 × 10⁹⁴(95-digit number)

52497260872527102079…32763647608097319001

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

1.049 × 10⁹⁵(96-digit number)

10499452174505420415…65527295216194637999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.049 × 10⁹⁵(96-digit number)

10499452174505420415…65527295216194638001

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

2.099 × 10⁹⁵(96-digit number)

20998904349010840831…31054590432389275999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.099 × 10⁹⁵(96-digit number)

20998904349010840831…31054590432389276001

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

4.199 × 10⁹⁵(96-digit number)

41997808698021681663…62109180864778551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.199 × 10⁹⁵(96-digit number)

41997808698021681663…62109180864778552001

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

8.399 × 10⁹⁵(96-digit number)

83995617396043363327…24218361729557103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.399 × 10⁹⁵(96-digit number)

83995617396043363327…24218361729557104001

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 #1,542,026

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