Block #566,361

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/28/2014, 9:17:15 PM · Difficulty 10.9659 · 6,229,634 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ba837f78af6ea3e0e35748dfd4d5052c71a0a2fc90df9456f3282e17013a0a7

View on Chainz ↗

Height

#566,361

Difficulty

10.965882

Transactions

Size

1.08 KB

Version

Bits

0af7440a

Nonce

63,215,586

Timestamp

5/28/2014, 9:17:15 PM

Confirmations

6,229,634

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

fc799371c6dc01dc64c7bacc9b0060fd3d05eb67322265018bcf4b879f03c13c

Transactions (5)

Coinbase3609eb082d1c5c…f187ae6ed7cecc

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

e1bd34becd986c…45ee0c80601ad1

1 in → 2 out6.7395 XPM225 B

AavZGGZK…yhsaPgX6 AHEQfvX1…TPvBMj6P

32a19a2d89fb98…4cca4c8ea1dd86

1 in → 2 out5.1926 XPM225 B

AYDitHPR…5PsRyTVs APbdJaha…FnDNQ5yE

123ede1a8f8d85…a4fa95dec842a2

1 in → 2 out5.5285 XPM226 B

AG8u7ddV…cU5QJSqk AG78dPKn…HCSwkc9e

2155d616b22fbc…095575ee5ae1a4

1 in → 2 out3.0158 XPM226 B

AcVexCzF…SY75pd2v AJ6j2oaw…3nQRmZEg

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.

9.259 × 10¹⁰¹(102-digit number)

92595344166647058915…29099053882227425279

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

9.259 × 10¹⁰¹(102-digit number)

92595344166647058915…29099053882227425279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.259 × 10¹⁰¹(102-digit number)

92595344166647058915…29099053882227425281

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

1.851 × 10¹⁰²(103-digit number)

18519068833329411783…58198107764454850559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.851 × 10¹⁰²(103-digit number)

18519068833329411783…58198107764454850561

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

3.703 × 10¹⁰²(103-digit number)

37038137666658823566…16396215528909701119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.703 × 10¹⁰²(103-digit number)

37038137666658823566…16396215528909701121

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

7.407 × 10¹⁰²(103-digit number)

74076275333317647132…32792431057819402239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.407 × 10¹⁰²(103-digit number)

74076275333317647132…32792431057819402241

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

1.481 × 10¹⁰³(104-digit number)

14815255066663529426…65584862115638804479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.481 × 10¹⁰³(104-digit number)

14815255066663529426…65584862115638804481

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