Block #476,274

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/5/2014, 5:51:00 PM · Difficulty 10.4703 · 6,314,878 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5940a2fc70dcf8b8db18329efc7a88bda87eda2cc11af4bc59e644fcd27342fe

View on Chainz ↗

Height

#476,274

Difficulty

10.470308

Transactions

Size

33.82 KB

Version

Bits

0a786615

Nonce

564,812

Timestamp

4/5/2014, 5:51:00 PM

Confirmations

6,314,878

Merkle Root

04c74e7482190d69cb747058f9e6f92271b67deef994c60a4374cf4145c44e6b

Transactions (3)

Coinbaseb08004330b8ff2…39b64c99aaba89

1 in → 1 out9.4700 XPM110 B

AeKNrjNj…1NEq95Ta

a31bffdb43c574…2999622c2e302e

5 in → 15 out45.7400 XPM1.06 KB

AUUPKMgH…9PwnJZJb AJKBP36r…iyiCcUAS AbTkHq49…Eo1k1gXY AUsL6VH6…Du8VQEdZ Aai7rmvE…JWhtS5Q5

0ab0bb06ab0898…3170dd1ef9b6e6

225 in → 1 out71.7042 XPM32.56 KB

AKXDjwi2…R8XB7jrs

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.

2.144 × 10⁹⁷(98-digit number)

21447865125789056466…02748917553347989999

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

2.144 × 10⁹⁷(98-digit number)

21447865125789056466…02748917553347989999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.144 × 10⁹⁷(98-digit number)

21447865125789056466…02748917553347990001

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

4.289 × 10⁹⁷(98-digit number)

42895730251578112932…05497835106695979999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.289 × 10⁹⁷(98-digit number)

42895730251578112932…05497835106695980001

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

8.579 × 10⁹⁷(98-digit number)

85791460503156225865…10995670213391959999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.579 × 10⁹⁷(98-digit number)

85791460503156225865…10995670213391960001

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

1.715 × 10⁹⁸(99-digit number)

17158292100631245173…21991340426783919999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.715 × 10⁹⁸(99-digit number)

17158292100631245173…21991340426783920001

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

3.431 × 10⁹⁸(99-digit number)

34316584201262490346…43982680853567839999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.431 × 10⁹⁸(99-digit number)

34316584201262490346…43982680853567840001

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