Block #447,312

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 5:14:55 AM · Difficulty 10.3543 · 6,366,850 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc64e6692441129752e24236bb423c6cf925c78da2a3f3997cc137fff6bf4b35

View on Chainz ↗

Height

#447,312

Difficulty

10.354274

Transactions

Size

903 B

Version

Bits

0a5ab1b7

Nonce

554,132

Timestamp

3/17/2014, 5:14:55 AM

Confirmations

6,366,850

Mined by

⛏️ PAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

d0eb0343b7deea05174d8ce1dc45d5c09d70eaebd3b5493a5108e44d214e3f13

Transactions (1)

Coinbased0eb0343b7deea…08e44d214e3f13

1 in → 22 out9.3100 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg AdoqUYAy…tJ482T9b AUFKXvnz…342ApNcm

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.

3.383 × 10⁹⁸(99-digit number)

33831052091403466105…81101077566656682559

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

3.383 × 10⁹⁸(99-digit number)

33831052091403466105…81101077566656682559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.383 × 10⁹⁸(99-digit number)

33831052091403466105…81101077566656682561

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

6.766 × 10⁹⁸(99-digit number)

67662104182806932211…62202155133313365119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.766 × 10⁹⁸(99-digit number)

67662104182806932211…62202155133313365121

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

1.353 × 10⁹⁹(100-digit number)

13532420836561386442…24404310266626730239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.353 × 10⁹⁹(100-digit number)

13532420836561386442…24404310266626730241

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

2.706 × 10⁹⁹(100-digit number)

27064841673122772884…48808620533253460479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.706 × 10⁹⁹(100-digit number)

27064841673122772884…48808620533253460481

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

5.412 × 10⁹⁹(100-digit number)

54129683346245545769…97617241066506920959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.412 × 10⁹⁹(100-digit number)

54129683346245545769…97617241066506920961

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 #447,312

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