Block #539,878

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/12/2014, 9:54:22 PM · Difficulty 10.9305 · 6,254,392 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

056d59acc60cff47c9488aa2432a27d77ed37d537574914a7a4903883baaab2c

View on Chainz ↗

Height

#539,878

Difficulty

10.930490

Transactions

Size

7.08 KB

Version

Bits

0aee3495

Nonce

648,198,234

Timestamp

5/12/2014, 9:54:22 PM

Confirmations

6,254,392

Merkle Root

436a4ae5144de3e84542c1fb3b314d6454fb4de3febedcb4668a1786f908aa73

Transactions (4)

Coinbase1fb3fec3bb88c8…1468e40483b58b

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

337639cdea117c…f61f07eb903aff

43 in → 2 out444.0114 XPM6.29 KB

AN45xKJb…jzPnBV6L AQAEKaSC…Uj8msJeB

8be3112c2df2ee…9f2a9d02c390b1

2 in → 2 out16.8000 XPM376 B

ALGPFRUq…E7BYC4Ba AJnLdNuf…3EQVEdGz

18480460085ef9…f9fea2d6738c40

1 in → 2 out8.3800 XPM225 B

AbPwn6hg…1zUiTuba AMfpBx29…Cxz69rez

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.

1.918 × 10⁹⁹(100-digit number)

19182293836144730314…02075131511831131199

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

1.918 × 10⁹⁹(100-digit number)

19182293836144730314…02075131511831131199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.918 × 10⁹⁹(100-digit number)

19182293836144730314…02075131511831131201

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

3.836 × 10⁹⁹(100-digit number)

38364587672289460628…04150263023662262399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.836 × 10⁹⁹(100-digit number)

38364587672289460628…04150263023662262401

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

7.672 × 10⁹⁹(100-digit number)

76729175344578921256…08300526047324524799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.672 × 10⁹⁹(100-digit number)

76729175344578921256…08300526047324524801

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

1.534 × 10¹⁰⁰(101-digit number)

15345835068915784251…16601052094649049599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.534 × 10¹⁰⁰(101-digit number)

15345835068915784251…16601052094649049601

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

3.069 × 10¹⁰⁰(101-digit number)

30691670137831568502…33202104189298099199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.069 × 10¹⁰⁰(101-digit number)

30691670137831568502…33202104189298099201

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