Block #479,858

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/7/2014, 11:02:43 PM · Difficulty 10.5105 · 6,326,656 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

efff0c5b886ee6b30c67563f0eb8a56e236b4ec6cdd8da4a36b52bccf693ead4

View on Chainz ↗

Height

#479,858

Difficulty

10.510458

Transactions

Size

867 B

Version

Bits

0a82ad59

Nonce

61,693

Timestamp

4/7/2014, 11:02:43 PM

Confirmations

6,326,656

Mined by

⛏️ rRaSC.v+AHwvxqCNvsnPA75eepHf4rKFfZ7z7foF67

Merkle Root

14e14eebfeeec5ff2a18683928bf2a8968ffd602d3a81aac18b75a9c28f4f20e

Transactions (1)

Coinbase14e14eebfeeec5…b75a9c28f4f20e

1 in → 21 out9.0400 XPM777 B

AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 AWMrD5hP…ZwsoxvZ3 ALqxX1WA…hsKjbnXn

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.

2.670 × 10⁹⁴(95-digit number)

26706982939574098816…88878224175709457919

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

2.670 × 10⁹⁴(95-digit number)

26706982939574098816…88878224175709457919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.670 × 10⁹⁴(95-digit number)

26706982939574098816…88878224175709457921

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

5.341 × 10⁹⁴(95-digit number)

53413965879148197633…77756448351418915839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.341 × 10⁹⁴(95-digit number)

53413965879148197633…77756448351418915841

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

1.068 × 10⁹⁵(96-digit number)

10682793175829639526…55512896702837831679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.068 × 10⁹⁵(96-digit number)

10682793175829639526…55512896702837831681

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

2.136 × 10⁹⁵(96-digit number)

21365586351659279053…11025793405675663359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.136 × 10⁹⁵(96-digit number)

21365586351659279053…11025793405675663361

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

4.273 × 10⁹⁵(96-digit number)

42731172703318558106…22051586811351326719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.273 × 10⁹⁵(96-digit number)

42731172703318558106…22051586811351326721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.546 × 10⁹⁵(96-digit number)

85462345406637116213…44103173622702653439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #479,858

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