Block #476,041

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 2:19:25 PM · Difficulty 10.4673 · 6,318,766 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f559ea80520de468d57e32bda0a0963261a215d306c5f379e0c40fd837f01be3

View on Chainz ↗

Height

#476,041

Difficulty

10.467263

Transactions

Size

885 B

Version

Bits

0a779e8f

Nonce

146,987,577

Timestamp

4/5/2014, 2:19:25 PM

Confirmations

6,318,766

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

db7cfddae4751c977eb9496242315c4c96a755499675154e2248edb82c270f72

Transactions (4)

Coinbase14c1d3dbb483a0…5f24ee111a6383

1 in → 1 out9.1400 XPM116 B

AbwWkWZt…kawDhufa

de73058b9a4477…be4a5b8b75d5d9

1 in → 2 out9.1500 XPM225 B

AXaZ6VTG…TGMPXAyT AJ9PvRK7…RSKR4o1S

9bbcf68499ee28…23ef45e340b644

1 in → 2 out9.1500 XPM227 B

AFneT83U…bH16atqo AXVqL4KM…bJPeTWdV

c5d09d5802de41…5af359a8e601fe

1 in → 2 out8.1394 XPM226 B

AeTde7fH…w7crTzqr AKf98qgL…WLUwe3RB

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.

4.934 × 10⁹⁷(98-digit number)

49346192470199007832…92383539475036325959

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

4.934 × 10⁹⁷(98-digit number)

49346192470199007832…92383539475036325959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.934 × 10⁹⁷(98-digit number)

49346192470199007832…92383539475036325961

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

9.869 × 10⁹⁷(98-digit number)

98692384940398015664…84767078950072651919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.869 × 10⁹⁷(98-digit number)

98692384940398015664…84767078950072651921

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

1.973 × 10⁹⁸(99-digit number)

19738476988079603132…69534157900145303839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.973 × 10⁹⁸(99-digit number)

19738476988079603132…69534157900145303841

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

3.947 × 10⁹⁸(99-digit number)

39476953976159206265…39068315800290607679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.947 × 10⁹⁸(99-digit number)

39476953976159206265…39068315800290607681

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

7.895 × 10⁹⁸(99-digit number)

78953907952318412531…78136631600581215359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.895 × 10⁹⁸(99-digit number)

78953907952318412531…78136631600581215361

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