Block #476,572

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 10:16:19 PM · Difficulty 10.4735 · 6,324,892 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef9a58b998beff2b7675dbf6d666a01bf3dd3fbea8ee52622da8f717f25b5661

View on Chainz ↗

Height

#476,572

Difficulty

10.473521

Transactions

Size

208 B

Version

Bits

0a7938ad

Nonce

78,198

Timestamp

4/5/2014, 10:16:19 PM

Confirmations

6,324,892

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

426ea2b6fd4f16575a0b580f66a2b3c1f668ef12f28c030471a8a2873dbdf634

Transactions (1)

Coinbase426ea2b6fd4f16…a8a2873dbdf634

1 in → 1 out9.1000 XPM116 B

AbwWkWZt…kawDhufa

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.

3.882 × 10¹⁰⁰(101-digit number)

38829723334812267720…30962340123986067199

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

3.882 × 10¹⁰⁰(101-digit number)

38829723334812267720…30962340123986067199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.882 × 10¹⁰⁰(101-digit number)

38829723334812267720…30962340123986067201

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

7.765 × 10¹⁰⁰(101-digit number)

77659446669624535440…61924680247972134399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.765 × 10¹⁰⁰(101-digit number)

77659446669624535440…61924680247972134401

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

1.553 × 10¹⁰¹(102-digit number)

15531889333924907088…23849360495944268799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.553 × 10¹⁰¹(102-digit number)

15531889333924907088…23849360495944268801

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

3.106 × 10¹⁰¹(102-digit number)

31063778667849814176…47698720991888537599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.106 × 10¹⁰¹(102-digit number)

31063778667849814176…47698720991888537601

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

6.212 × 10¹⁰¹(102-digit number)

62127557335699628352…95397441983777075199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.212 × 10¹⁰¹(102-digit number)

62127557335699628352…95397441983777075201

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