Block #578,516

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/6/2014, 2:59:47 AM · Difficulty 10.9682 · 6,216,468 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d068960ecdab8e91edb9c6f4e3b8f69c61db7a959f61d38b98595912926de2b5

View on Chainz ↗

Height

#578,516

Difficulty

10.968183

Transactions

Size

434 B

Version

Bits

0af7dad2

Nonce

750,416,552

Timestamp

6/6/2014, 2:59:47 AM

Confirmations

6,216,468

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

74b20418e36e492b884e7d061e1305f4c3c358964c0609129ba78550f16d04ae

Transactions (2)

Coinbase9043e73479b0e4…d23e5bd3309a5a

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

c62600bfbc5d12…f336d95d7ad65f

1 in → 2 out1.9111 XPM225 B

AFxBZHFF…bozLmwZH AQYfM6tR…wtD7VsKo

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.

6.709 × 10¹⁰⁰(101-digit number)

67098760274831189249…42987085788649881599

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

6.709 × 10¹⁰⁰(101-digit number)

67098760274831189249…42987085788649881599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.709 × 10¹⁰⁰(101-digit number)

67098760274831189249…42987085788649881601

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

1.341 × 10¹⁰¹(102-digit number)

13419752054966237849…85974171577299763199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.341 × 10¹⁰¹(102-digit number)

13419752054966237849…85974171577299763201

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

2.683 × 10¹⁰¹(102-digit number)

26839504109932475699…71948343154599526399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.683 × 10¹⁰¹(102-digit number)

26839504109932475699…71948343154599526401

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

5.367 × 10¹⁰¹(102-digit number)

53679008219864951399…43896686309199052799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.367 × 10¹⁰¹(102-digit number)

53679008219864951399…43896686309199052801

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

1.073 × 10¹⁰²(103-digit number)

10735801643972990279…87793372618398105599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.073 × 10¹⁰²(103-digit number)

10735801643972990279…87793372618398105601

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