Block #448,245

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 7:11:31 PM · Difficulty 10.3669 · 6,346,148 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d93efbe88ea56e64a6173d202643f80164a054ed5560dba7a2cf28a513f27629

View on Chainz ↗

Height

#448,245

Difficulty

10.366914

Transactions

Size

1004 B

Version

Bits

0a5dee0d

Nonce

28,122

Timestamp

3/17/2014, 7:11:31 PM

Confirmations

6,346,148

Mined by

⛏️ aS'HAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

242c5ca6410e8f2bdda91363a76f170d6b25a9696dfed5b7cecaef9a0021970b

Transactions (1)

Coinbase242c5ca6410e8f…caef9a0021970b

1 in → 25 out9.2900 XPM913 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 AWMrD5hP…ZwsoxvZ3

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.

2.397 × 10⁹⁷(98-digit number)

23979532158196531960…14686720324238504959

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

2.397 × 10⁹⁷(98-digit number)

23979532158196531960…14686720324238504959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.397 × 10⁹⁷(98-digit number)

23979532158196531960…14686720324238504961

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

4.795 × 10⁹⁷(98-digit number)

47959064316393063921…29373440648477009919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.795 × 10⁹⁷(98-digit number)

47959064316393063921…29373440648477009921

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

9.591 × 10⁹⁷(98-digit number)

95918128632786127842…58746881296954019839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.591 × 10⁹⁷(98-digit number)

95918128632786127842…58746881296954019841

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

1.918 × 10⁹⁸(99-digit number)

19183625726557225568…17493762593908039679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.918 × 10⁹⁸(99-digit number)

19183625726557225568…17493762593908039681

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

3.836 × 10⁹⁸(99-digit number)

38367251453114451136…34987525187816079359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.836 × 10⁹⁸(99-digit number)

38367251453114451136…34987525187816079361

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