Block #477,964

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/6/2014, 6:57:27 PM · Difficulty 10.4895 · 6,313,481 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dadb51908caef48f7e9db25194ef5f76734ca0b508d55ebad933beafd612c304

View on Chainz ↗

Height

#477,964

Difficulty

10.489486

Transactions

Size

1.02 KB

Version

Bits

0a7d4ef8

Nonce

31,874

Timestamp

4/6/2014, 6:57:27 PM

Confirmations

6,313,481

Merkle Root

279d1b8f05748e1c99b1d5ebb5a335ff5a302a3d7faf3f4257ea99b168dd2663

Transactions (2)

Coinbase64be5fbc00c1ca…b4af25981708e3

1 in → 1 out9.0800 XPM110 B

AeKNrjNj…1NEq95Ta

ed4c9ca6307d75…a11ed97b0f88ca

4 in → 10 out30.3478 XPM843 B

ASPjZ7gM…AsC3LAuT AUHFmvnF…juaRoiLd Ac3rx7qQ…kQFJXueb AGw7KuTT…ZfJmwhoB AeKNrjNj…1NEq95Ta

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.

3.162 × 10¹⁰⁰(101-digit number)

31626554378631717424…09444949153369175519

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

3.162 × 10¹⁰⁰(101-digit number)

31626554378631717424…09444949153369175519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.162 × 10¹⁰⁰(101-digit number)

31626554378631717424…09444949153369175521

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

6.325 × 10¹⁰⁰(101-digit number)

63253108757263434849…18889898306738351039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.325 × 10¹⁰⁰(101-digit number)

63253108757263434849…18889898306738351041

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

1.265 × 10¹⁰¹(102-digit number)

12650621751452686969…37779796613476702079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.265 × 10¹⁰¹(102-digit number)

12650621751452686969…37779796613476702081

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

2.530 × 10¹⁰¹(102-digit number)

25301243502905373939…75559593226953404159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.530 × 10¹⁰¹(102-digit number)

25301243502905373939…75559593226953404161

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

5.060 × 10¹⁰¹(102-digit number)

50602487005810747879…51119186453906808319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.060 × 10¹⁰¹(102-digit number)

50602487005810747879…51119186453906808321

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