Block #515,872

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/29/2014, 1:08:41 AM · Difficulty 10.8436 · 6,285,121 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

aa18b5cd2d66534b92df34ad8fd6dffec41727f0c9699ca93390eb5889e08a50

View on Chainz ↗

Height

#515,872

Difficulty

10.843572

Transactions

Size

2.03 KB

Version

Bits

0ad7f45c

Nonce

68,095,289

Timestamp

4/29/2014, 1:08:41 AM

Confirmations

6,285,121

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

39eb16051f771d1ed3a6cfd8c7e1bb343582b41e947a0dd26e44cbd4d0eebb24

Transactions (4)

Coinbasef73f058e3d49e0…05570e8f07c5e5

1 in → 1 out8.5300 XPM116 B

AbwWkWZt…kawDhufa

3173cc8eaf2c13…b95a33f71e492e

1 in → 2 out5.1874 XPM226 B

ARrp3L34…Wcs6pfJC AXnL68UR…jsxeGUhN

a5841b3a5c35af…e3bc54dcb629ea

1 in → 2 out3.1766 XPM227 B

AXHMxTzm…qeW2xynz AZEXWBNM…jua3TF4w

aad0e09f67d0d2…eec4768ccdc158

9 in → 2 out1.0298 XPM1.38 KB

AZkJunJU…GJDPc9Hk Ac24WwPt…BSeTbxUj

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.

2.304 × 10¹⁰¹(102-digit number)

23049116783875689271…64322892471148011519

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

2.304 × 10¹⁰¹(102-digit number)

23049116783875689271…64322892471148011519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.304 × 10¹⁰¹(102-digit number)

23049116783875689271…64322892471148011521

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

4.609 × 10¹⁰¹(102-digit number)

46098233567751378542…28645784942296023039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.609 × 10¹⁰¹(102-digit number)

46098233567751378542…28645784942296023041

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

9.219 × 10¹⁰¹(102-digit number)

92196467135502757084…57291569884592046079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.219 × 10¹⁰¹(102-digit number)

92196467135502757084…57291569884592046081

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

1.843 × 10¹⁰²(103-digit number)

18439293427100551416…14583139769184092159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.843 × 10¹⁰²(103-digit number)

18439293427100551416…14583139769184092161

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

3.687 × 10¹⁰²(103-digit number)

36878586854201102833…29166279538368184319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.687 × 10¹⁰²(103-digit number)

36878586854201102833…29166279538368184321

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