Block #479,202

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 1:23:47 PM · Difficulty 10.5025 · 6,326,570 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99bd2d2607490a0e22ff6b2796431f13022aeb3207ed564b86554af37c1e9667

View on Chainz ↗

Height

#479,202

Difficulty

10.502502

Transactions

Size

868 B

Version

Bits

0a80a3fd

Nonce

69,576

Timestamp

4/7/2014, 1:23:47 PM

Confirmations

6,326,570

Mined by

⛏️ OjZAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

db877eaf379fac20b47b5980f443fc5db10f8a40c92c91d7b26ecab6e3692b21

Transactions (1)

Coinbasedb877eaf379fac…6ecab6e3692b21

1 in → 21 out9.0500 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AUzEPJFG…kYkA5U9V AZr7Ptuw…CM4Yw5jq AbHY4iza…Yckt2J5W

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.

1.384 × 10⁹⁶(97-digit number)

13849098637712220607…31976197584418882299

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

1.384 × 10⁹⁶(97-digit number)

13849098637712220607…31976197584418882299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.384 × 10⁹⁶(97-digit number)

13849098637712220607…31976197584418882301

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

2.769 × 10⁹⁶(97-digit number)

27698197275424441215…63952395168837764599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.769 × 10⁹⁶(97-digit number)

27698197275424441215…63952395168837764601

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

5.539 × 10⁹⁶(97-digit number)

55396394550848882430…27904790337675529199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.539 × 10⁹⁶(97-digit number)

55396394550848882430…27904790337675529201

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

1.107 × 10⁹⁷(98-digit number)

11079278910169776486…55809580675351058399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.107 × 10⁹⁷(98-digit number)

11079278910169776486…55809580675351058401

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

2.215 × 10⁹⁷(98-digit number)

22158557820339552972…11619161350702116799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.215 × 10⁹⁷(98-digit number)

22158557820339552972…11619161350702116801

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