Block #467,693

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/30/2014, 11:30:14 PM · Difficulty 10.4345 · 6,342,684 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3539ea79b5145e2d9c1758bf2330889664239dd50bd62c36d454187ad7f33a8c

View on Chainz ↗

Height

#467,693

Difficulty

10.434491

Transactions

Size

1.61 KB

Version

Bits

0a6f3ac6

Nonce

132,721

Timestamp

3/30/2014, 11:30:14 PM

Confirmations

6,342,684

Mined by

⛏️ "aS8AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

c983ff9449f6cf9b13320c460bf77c607a1e4804502ce74c48f84df8a29eceb2

Transactions (4)

Coinbasef1d07f63151cc1…1f0f2714141392

1 in → 24 out9.1700 XPM879 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AJzWx2VD…j4ZSMit5

2d872403af3797…12a6e351b4a4eb

1 in → 2 out15.0790 XPM227 B

AdUwUPP6…wS2d4W3h AHpdwqzz…iqCbkaFc

133b33b29b1c46…6d20eb2dacc144

1 in → 2 out15.0119 XPM225 B

AJw35xru…ycZrRP8Y AYCPhSk4…kUwyYZ2Z

1ce2c73175ed10…c84248cbbb5e16

1 in → 2 out14.9574 XPM226 B

AYgK6hP8…VracoMKq Aa7ubJso…coSnkggR

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.

2.153 × 10⁹²(93-digit number)

21534898474498175805…40129235790514815999

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

2.153 × 10⁹²(93-digit number)

21534898474498175805…40129235790514815999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.153 × 10⁹²(93-digit number)

21534898474498175805…40129235790514816001

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

4.306 × 10⁹²(93-digit number)

43069796948996351611…80258471581029631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.306 × 10⁹²(93-digit number)

43069796948996351611…80258471581029632001

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

8.613 × 10⁹²(93-digit number)

86139593897992703223…60516943162059263999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.613 × 10⁹²(93-digit number)

86139593897992703223…60516943162059264001

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

1.722 × 10⁹³(94-digit number)

17227918779598540644…21033886324118527999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.722 × 10⁹³(94-digit number)

17227918779598540644…21033886324118528001

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

3.445 × 10⁹³(94-digit number)

34455837559197081289…42067772648237055999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.445 × 10⁹³(94-digit number)

34455837559197081289…42067772648237056001

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

Block #467,693

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