Block #454,998

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 7:37:28 AM · Difficulty 10.4010 · 6,351,916 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

256f1a4854db0477664c8d9426543c249bf82bf82419f3525518be7088a072e6

View on Chainz ↗

Height

#454,998

Difficulty

10.401008

Transactions

Size

936 B

Version

Bits

0a66a876

Nonce

294,729

Timestamp

3/22/2014, 7:37:28 AM

Confirmations

6,351,916

Mined by

⛏️ VaS-=}xAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

1d8215ba7bcc575b89c5ea70dda777df087e5886dda336d74d8918c2ffd8a06e

Transactions (1)

Coinbase1d8215ba7bcc57…8918c2ffd8a06e

1 in → 23 out9.2300 XPM845 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AdhWfaX2…aX7YvEJq

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.

1.563 × 10⁹⁶(97-digit number)

15635786890083799090…42002154268850175999

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

1.563 × 10⁹⁶(97-digit number)

15635786890083799090…42002154268850175999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.563 × 10⁹⁶(97-digit number)

15635786890083799090…42002154268850176001

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

3.127 × 10⁹⁶(97-digit number)

31271573780167598180…84004308537700351999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.127 × 10⁹⁶(97-digit number)

31271573780167598180…84004308537700352001

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

6.254 × 10⁹⁶(97-digit number)

62543147560335196360…68008617075400703999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.254 × 10⁹⁶(97-digit number)

62543147560335196360…68008617075400704001

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

1.250 × 10⁹⁷(98-digit number)

12508629512067039272…36017234150801407999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.250 × 10⁹⁷(98-digit number)

12508629512067039272…36017234150801408001

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

2.501 × 10⁹⁷(98-digit number)

25017259024134078544…72034468301602815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.501 × 10⁹⁷(98-digit number)

25017259024134078544…72034468301602816001

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 #454,998

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