Block #473,979

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/4/2014, 7:05:14 AM · Difficulty 10.4462 · 6,322,671 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0312b4c62d66821941f6330fb040b2e51849367eff054cf451fdbcf2cf06f6e4

View on Chainz ↗

Height

#473,979

Difficulty

10.446217

Transactions

Size

1.07 KB

Version

Bits

0a723b3f

Nonce

77,522

Timestamp

4/4/2014, 7:05:14 AM

Confirmations

6,322,671

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

4380a7c9bec1342ec61ceedb15adf0a2e0d8c02937d5b5677896a1b3c941d8e8

Transactions (3)

Coinbasea99c042e85da4c…bdb12f05797268

1 in → 1 out9.1710 XPM116 B

AbwWkWZt…kawDhufa

5e86eecdad8d91…8add8ffdbb1885

3 in → 10 out27.6200 XPM692 B

AHDXF3Ls…Vg5V84qr APgnf8g1…pc1dKR4J AGjbCUpe…KtN4LdVP ASu16mM2…HMZ4nzyA AeKNrjNj…1NEq95Ta

8b664d4399388c…6bcf218ff83d29

1 in → 1 out0.9900 XPM192 B

AUZteVJG…8ZcnDH77

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.

1.346 × 10⁹⁶(97-digit number)

13464129836972202902…91853564606044635519

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

1.346 × 10⁹⁶(97-digit number)

13464129836972202902…91853564606044635519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.346 × 10⁹⁶(97-digit number)

13464129836972202902…91853564606044635521

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

2.692 × 10⁹⁶(97-digit number)

26928259673944405804…83707129212089271039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.692 × 10⁹⁶(97-digit number)

26928259673944405804…83707129212089271041

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

5.385 × 10⁹⁶(97-digit number)

53856519347888811608…67414258424178542079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.385 × 10⁹⁶(97-digit number)

53856519347888811608…67414258424178542081

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

1.077 × 10⁹⁷(98-digit number)

10771303869577762321…34828516848357084159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.077 × 10⁹⁷(98-digit number)

10771303869577762321…34828516848357084161

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

2.154 × 10⁹⁷(98-digit number)

21542607739155524643…69657033696714168319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.154 × 10⁹⁷(98-digit number)

21542607739155524643…69657033696714168321

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