Block #64,020

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 5:12:28 AM · Difficulty 8.9806 · 6,726,036 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cf1e0b89cca552f564433d1989d69700866985e106a2101d5b21c7a7bcd8092d

View on Chainz ↗

Height

#64,020

Difficulty

8.980617

Transactions

Size

2.47 KB

Version

Bits

08fb09b2

Nonce

382

Timestamp

7/19/2013, 5:12:28 AM

Confirmations

6,726,036

Merkle Root

ef7e0864c965df7ab36d9ed37eb417dabd21ea7a99a7f3d2386f693f12ed6716

Transactions (4)

Coinbasedb3032207d3337…289203c8eb004d

1 in → 1 out12.4200 XPM110 B

AZ5HQjDF…BZwojg5F

28fce904177c7c…45c4ad6d53143e

10 in → 2 out1637.3717 XPM1.52 KB

AJS1kqGJ…QGof3PaR ANLbqcgt…7DXjqmGL

d7a6ed02b3e807…238c6b8ec0f5bd

1 in → 1 out15.6300 XPM158 B

AKjY5JYV…xhK7yPrn

494e36f5c46461…d50cecf9cd12d5

5 in → 1 out62.1000 XPM612 B

ALp4QBZx…yAnNHja9

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.

4.257 × 10⁹¹(92-digit number)

42575888043415203856…92476176034586895539

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

4.257 × 10⁹¹(92-digit number)

42575888043415203856…92476176034586895539

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.257 × 10⁹¹(92-digit number)

42575888043415203856…92476176034586895541

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

8.515 × 10⁹¹(92-digit number)

85151776086830407713…84952352069173791079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.515 × 10⁹¹(92-digit number)

85151776086830407713…84952352069173791081

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

1.703 × 10⁹²(93-digit number)

17030355217366081542…69904704138347582159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.703 × 10⁹²(93-digit number)

17030355217366081542…69904704138347582161

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

3.406 × 10⁹²(93-digit number)

34060710434732163085…39809408276695164319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.406 × 10⁹²(93-digit number)

34060710434732163085…39809408276695164321

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

6.812 × 10⁹²(93-digit number)

68121420869464326170…79618816553390328639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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