Block #479,977

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/8/2014, 12:55:42 AM · Difficulty 10.5113 · 6,323,359 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d34ec0f0e1e37a7b80029295cbdf96af70fabeda2820edf036c646e666b96e61

View on Chainz ↗

Height

#479,977

Difficulty

10.511254

Transactions

Size

1.15 KB

Version

Bits

0a82e18c

Nonce

20,891,102

Timestamp

4/8/2014, 12:55:42 AM

Confirmations

6,323,359

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

fe64ac8995de77cc1435e3ebc069f5b07e1934f5e58245cb014527d8d441e918

Transactions (4)

Coinbase501b57336685c4…df2318bda06988

1 in → 1 out9.0700 XPM116 B

AbwWkWZt…kawDhufa

9dc8d6cf3b7b9f…b0a699965b13ce

3 in → 2 out1111.0000 XPM522 B

AKrKmUfb…jUQpKaoH AKeTg3m1…Bvsv2sV1

f7b65f2f480cc5…47b7ca09214b31

1 in → 2 out8.5799 XPM227 B

AVR9s4fa…AW7C55ZT AJ5vgFDp…9GjcHxsU

4dd503702ee198…15a2da897da08a

1 in → 2 out6.5548 XPM226 B

AX7868xY…HaHAn3Yo AT9FqoUV…fowL4nC3

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.

4.578 × 10⁹⁷(98-digit number)

45786376946730055693…96258512081498300679

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

4.578 × 10⁹⁷(98-digit number)

45786376946730055693…96258512081498300679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.578 × 10⁹⁷(98-digit number)

45786376946730055693…96258512081498300681

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

9.157 × 10⁹⁷(98-digit number)

91572753893460111386…92517024162996601359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.157 × 10⁹⁷(98-digit number)

91572753893460111386…92517024162996601361

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

1.831 × 10⁹⁸(99-digit number)

18314550778692022277…85034048325993202719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.831 × 10⁹⁸(99-digit number)

18314550778692022277…85034048325993202721

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

3.662 × 10⁹⁸(99-digit number)

36629101557384044554…70068096651986405439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.662 × 10⁹⁸(99-digit number)

36629101557384044554…70068096651986405441

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

7.325 × 10⁹⁸(99-digit number)

73258203114768089109…40136193303972810879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.325 × 10⁹⁸(99-digit number)

73258203114768089109…40136193303972810881

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