Block #481,026

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/8/2014, 3:38:32 PM · Difficulty 10.5272 · 6,327,627 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f85c52a9348d91a4f45fe0d7dc379c3cfd097c364328358a0d9ecb4bcf57e641

View on Chainz ↗

Height

#481,026

Difficulty

10.527189

Transactions

Size

1.08 KB

Version

Bits

0a86f5e2

Nonce

212,744,572

Timestamp

4/8/2014, 3:38:32 PM

Confirmations

6,327,627

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

9b22541f1a1bb8e55a7915be998af33ca7c7493352369801790b828f588ad73f

Transactions (5)

Coinbased35d83b1539a3a…e88cb6ebf9ad57

1 in → 1 out9.0500 XPM116 B

AbwWkWZt…kawDhufa

a8fc6882f1dea8…c31daeaa027faa

1 in → 2 out6.9008 XPM226 B

APjgy8Mm…kC5BpgKE AbEQGvmq…aPHsEzwc

e7eb1e73966b51…40082b332f7fb7

1 in → 2 out7.0487 XPM225 B

ALGFjqHN…55bE6ZTs ATDXCeGZ…A112cy7M

3981562e73260b…8d0724798251c0

1 in → 2 out7.0410 XPM225 B

AHt2xB4g…TLho1X8P AFsG7qGi…YPTSYiHB

9258957d10f77e…6d8f3f949329b5

1 in → 2 out7.0268 XPM226 B

AXY8EgiU…keGzENVf AQLYJjWd…uXnStjKQ

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.

1.308 × 10⁹⁷(98-digit number)

13088055237558307809…49227784834363110099

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

1.308 × 10⁹⁷(98-digit number)

13088055237558307809…49227784834363110099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.308 × 10⁹⁷(98-digit number)

13088055237558307809…49227784834363110101

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

2.617 × 10⁹⁷(98-digit number)

26176110475116615619…98455569668726220199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.617 × 10⁹⁷(98-digit number)

26176110475116615619…98455569668726220201

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

5.235 × 10⁹⁷(98-digit number)

52352220950233231238…96911139337452440399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.235 × 10⁹⁷(98-digit number)

52352220950233231238…96911139337452440401

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

1.047 × 10⁹⁸(99-digit number)

10470444190046646247…93822278674904880799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.047 × 10⁹⁸(99-digit number)

10470444190046646247…93822278674904880801

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

2.094 × 10⁹⁸(99-digit number)

20940888380093292495…87644557349809761599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.094 × 10⁹⁸(99-digit number)

20940888380093292495…87644557349809761601

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 #481,026

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