Block #478,335

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/7/2014, 12:35:15 AM · Difficulty 10.4925 · 6,330,969 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

009a946030abd2da66365818caeaa7405f8c76c7c05984cb1f8844f61ec82c09

View on Chainz ↗

Height

#478,335

Difficulty

10.492516

Transactions

Size

1.83 KB

Version

Bits

0a7e158c

Nonce

178,205,453

Timestamp

4/7/2014, 12:35:15 AM

Confirmations

6,330,969

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

9fa70e6594292ae355ace7b30decbb79d039382e89e0cad0e2d9918a27a69fa2

Transactions (5)

Coinbasefa57189d0fbd44…2eacd154a3a5f1

1 in → 1 out9.1200 XPM116 B

AbwWkWZt…kawDhufa

514799e75c5c73…5b027fcc71c1bf

4 in → 10 out28.2678 XPM837 B

ASu16mM2…HMZ4nzyA AQpF1vAG…Zo8pfzv2 Ab2TQhM2…MChPbEoL AJrZAsFD…mqWWUUnE AJ1Rg4tk…5YkqEmTH

042df11c868407…c00a700e441e7e

1 in → 2 out6.5697 XPM225 B

ALUvR7Wq…2NCZfJdA Ac24WwPt…BSeTbxUj

6c4f30240d7b6d…7392c4a410105a

1 in → 2 out5.0219 XPM226 B

AYasAqhp…f99B4Jti AMhGLGfw…WRvopSHk

c64ee4f720c14d…6a59e819436ace

2 in → 2 out0.7375 XPM374 B

ANZkPFPo…SMDbeh7T ANnZ2Fng…Hngj99t5

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.

9.705 × 10⁹⁷(98-digit number)

97055282456424216317…56913187764467637999

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

9.705 × 10⁹⁷(98-digit number)

97055282456424216317…56913187764467637999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.705 × 10⁹⁷(98-digit number)

97055282456424216317…56913187764467638001

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

1.941 × 10⁹⁸(99-digit number)

19411056491284843263…13826375528935275999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.941 × 10⁹⁸(99-digit number)

19411056491284843263…13826375528935276001

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

3.882 × 10⁹⁸(99-digit number)

38822112982569686526…27652751057870551999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.882 × 10⁹⁸(99-digit number)

38822112982569686526…27652751057870552001

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

7.764 × 10⁹⁸(99-digit number)

77644225965139373053…55305502115741103999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.764 × 10⁹⁸(99-digit number)

77644225965139373053…55305502115741104001

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

1.552 × 10⁹⁹(100-digit number)

15528845193027874610…10611004231482207999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.552 × 10⁹⁹(100-digit number)

15528845193027874610…10611004231482208001

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

Block #478,335

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