Block #542,748

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/14/2014, 2:29:23 AM · Difficulty 10.9448 · 6,267,126 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

210dbd9f58ec00560ec5ae759f7c131d0e588f7e65ae4c5f4161a36aad3c8df1

View on Chainz ↗

Height

#542,748

Difficulty

10.944812

Transactions

Size

3.60 KB

Version

Bits

0af1df33

Nonce

227,948,716

Timestamp

5/14/2014, 2:29:23 AM

Confirmations

6,267,126

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

424a52a4ae13147c5366153ea3ae2d49f9cefdad90fc9b0a2f61865770cc3638

Transactions (2)

Coinbase3b90ad8ffd2e96…0bb12a1a849cf7

1 in → 1 out8.3700 XPM116 B

ANSXnLY2…Sd25TjkD

3e686b9e3364c0…1c033e7a65eb68

23 in → 2 out25.6873 XPM3.40 KB

ARftmR3m…HdhJfZYr AXRU71Bb…CCZiSoqj

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.

1.517 × 10¹⁰¹(102-digit number)

15175870287512188367…81735780712632156159

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

1.517 × 10¹⁰¹(102-digit number)

15175870287512188367…81735780712632156159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.517 × 10¹⁰¹(102-digit number)

15175870287512188367…81735780712632156161

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

3.035 × 10¹⁰¹(102-digit number)

30351740575024376735…63471561425264312319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.035 × 10¹⁰¹(102-digit number)

30351740575024376735…63471561425264312321

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

6.070 × 10¹⁰¹(102-digit number)

60703481150048753470…26943122850528624639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.070 × 10¹⁰¹(102-digit number)

60703481150048753470…26943122850528624641

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

1.214 × 10¹⁰²(103-digit number)

12140696230009750694…53886245701057249279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.214 × 10¹⁰²(103-digit number)

12140696230009750694…53886245701057249281

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

2.428 × 10¹⁰²(103-digit number)

24281392460019501388…07772491402114498559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.428 × 10¹⁰²(103-digit number)

24281392460019501388…07772491402114498561

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 #542,748

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