Block #539,046

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/12/2014, 1:55:17 PM · Difficulty 10.9254 · 6,259,117 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b3bf7d281d7c51fbcc28ef064a0a36c837217f1e530a447089b3ec8805a3ef20

View on Chainz ↗

Height

#539,046

Difficulty

10.925430

Transactions

Size

807 B

Version

Bits

0aece902

Nonce

81,564,788

Timestamp

5/12/2014, 1:55:17 PM

Confirmations

6,259,117

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

12f9a934ef425f8b9d2ad3e51e99e3116898845c4e61c13dee18f33066fe5cf3

Transactions (3)

Coinbase04b6253c71c7ce…07296a9dd2915f

1 in → 1 out8.3800 XPM116 B

ANSXnLY2…Sd25TjkD

deabecbdc93283…a4fcf5fb46c2d1

2 in → 2 out3.1841 XPM373 B

AeKNrjNj…1NEq95Ta AHZj6GaQ…p5zDySQg

ea0422cfbfb05a…639028b829c4cf

1 in → 2 out3.4143 XPM226 B

ATRgZH3d…wErJY9eP AGdWVjRk…LFVsqCnK

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.

3.403 × 10⁹⁸(99-digit number)

34036651556066228734…66047214456795828719

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

3.403 × 10⁹⁸(99-digit number)

34036651556066228734…66047214456795828719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.403 × 10⁹⁸(99-digit number)

34036651556066228734…66047214456795828721

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

6.807 × 10⁹⁸(99-digit number)

68073303112132457468…32094428913591657439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.807 × 10⁹⁸(99-digit number)

68073303112132457468…32094428913591657441

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

1.361 × 10⁹⁹(100-digit number)

13614660622426491493…64188857827183314879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.361 × 10⁹⁹(100-digit number)

13614660622426491493…64188857827183314881

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

2.722 × 10⁹⁹(100-digit number)

27229321244852982987…28377715654366629759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.722 × 10⁹⁹(100-digit number)

27229321244852982987…28377715654366629761

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

5.445 × 10⁹⁹(100-digit number)

54458642489705965974…56755431308733259519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.445 × 10⁹⁹(100-digit number)

54458642489705965974…56755431308733259521

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