Block #533,345

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/9/2014, 3:54:25 PM · Difficulty 10.8994 · 6,262,732 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

46befebb823c9ebcac7f1383865a49a362bfada1ed30ad6d7a9786a63048328f

View on Chainz ↗

Height

#533,345

Difficulty

10.899387

Transactions

Size

808 B

Version

Bits

0ae63e34

Nonce

87,613,722

Timestamp

5/9/2014, 3:54:25 PM

Confirmations

6,262,732

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

53b60f0d6c1ddd2696450cf76c8863f0c4d32507c1fce49a02f3ecf573e70965

Transactions (3)

Coinbase00cce6044deff5…e9178bb8a37d88

1 in → 1 out8.4200 XPM116 B

ANSXnLY2…Sd25TjkD

2b8d451b42c7be…5aeb87c1e4acbb

1 in → 2 out3.3239 XPM225 B

AYMFvqra…jqsU66Vu AeHmxERP…2hhYf2ho

4547fa822148da…0ce57579dc440b

2 in → 2 out1.0921 XPM375 B

AG3TPGas…cJvesb2o ATcW9KKf…4Es7A1oQ

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.

2.334 × 10⁹⁹(100-digit number)

23344854726920348649…63962201356314430559

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

2.334 × 10⁹⁹(100-digit number)

23344854726920348649…63962201356314430559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.334 × 10⁹⁹(100-digit number)

23344854726920348649…63962201356314430561

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

4.668 × 10⁹⁹(100-digit number)

46689709453840697298…27924402712628861119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.668 × 10⁹⁹(100-digit number)

46689709453840697298…27924402712628861121

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

9.337 × 10⁹⁹(100-digit number)

93379418907681394596…55848805425257722239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.337 × 10⁹⁹(100-digit number)

93379418907681394596…55848805425257722241

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

1.867 × 10¹⁰⁰(101-digit number)

18675883781536278919…11697610850515444479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.867 × 10¹⁰⁰(101-digit number)

18675883781536278919…11697610850515444481

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

3.735 × 10¹⁰⁰(101-digit number)

37351767563072557838…23395221701030888959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.735 × 10¹⁰⁰(101-digit number)

37351767563072557838…23395221701030888961

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