Block #568,024

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/30/2014, 2:56:34 AM · Difficulty 10.9651 · 6,237,781 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a8da4b544a2562875e00502a1cfb6975a1b02681951e23a734dc9ca394531850

View on Chainz ↗

Height

#568,024

Difficulty

10.965144

Transactions

Size

1.37 KB

Version

Bits

0af713aa

Nonce

236,295

Timestamp

5/30/2014, 2:56:34 AM

Confirmations

6,237,781

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e71ad2277e3b2e5c245d4cb58a184e60aea99a23ce2ad0fa885591eada4e375c

Transactions (5)

Coinbased408cdc77227bf…bbe93649c605a2

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

52c529d9f45db2…845743a5bd1a51

3 in → 2 out22.0124 XPM522 B

AZCBfoK2…3M9L6mMt AZkTRBEd…r4CQEyeh

c9d3075f6b324f…c57aa89832aa35

1 in → 2 out5.0640 XPM225 B

AenGiSGP…VmaExxbt AayZNdB8…ki6iLXiv

3679e7ba0e005c…aa8d43e3b01878

1 in → 2 out7.2609 XPM226 B

AZcbtVdK…DBQpQGv2 AWB1ZURv…yJ1zH7Mc

1e5f4c1eb66c07…a1282b5dbed45b

1 in → 2 out1.4007 XPM226 B

AWsLmT7m…KrmHXwmG AM23VEk3…q622MtoH

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.

1.654 × 10⁹⁷(98-digit number)

16544533483445856049…86717889280017995999

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

1.654 × 10⁹⁷(98-digit number)

16544533483445856049…86717889280017995999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.654 × 10⁹⁷(98-digit number)

16544533483445856049…86717889280017996001

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

3.308 × 10⁹⁷(98-digit number)

33089066966891712099…73435778560035991999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.308 × 10⁹⁷(98-digit number)

33089066966891712099…73435778560035992001

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

6.617 × 10⁹⁷(98-digit number)

66178133933783424199…46871557120071983999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.617 × 10⁹⁷(98-digit number)

66178133933783424199…46871557120071984001

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

1.323 × 10⁹⁸(99-digit number)

13235626786756684839…93743114240143967999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.323 × 10⁹⁸(99-digit number)

13235626786756684839…93743114240143968001

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

2.647 × 10⁹⁸(99-digit number)

26471253573513369679…87486228480287935999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.647 × 10⁹⁸(99-digit number)

26471253573513369679…87486228480287936001

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