Block #568,497

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/30/2014, 11:13:29 AM · Difficulty 10.9650 · 6,239,882 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5295b378e341818253fb56b971d96ea5a2085a5cc1d1771f7d9d5babe881e9e3

View on Chainz ↗

Height

#568,497

Difficulty

10.964976

Transactions

Size

1.22 KB

Version

Bits

0af708a8

Nonce

32,822,435

Timestamp

5/30/2014, 11:13:29 AM

Confirmations

6,239,882

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2572c7e68411dde2d2ded7a15be2c24ce212052a5bf31dcc269ea09638287f6f

Transactions (3)

Coinbaseb325bf6712b023…9b8e0b6ec7b106

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

e8d42e13ddf374…25dd8dbcc2da2b

4 in → 1 out150.0000 XPM636 B

ATkWsDnQ…Wz8yMvLp

96e6adb6919090…57fb58bdd2b258

2 in → 4 out10.5271 XPM407 B

AVwEv1Mr…hDdRarHN Ad5rowoZ…YCVsFMcc AeKNrjNj…1NEq95Ta AcacZaAu…7XaX5VD6

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.

3.987 × 10⁹⁷(98-digit number)

39873852606899247836…38037498715707718919

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

3.987 × 10⁹⁷(98-digit number)

39873852606899247836…38037498715707718919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.987 × 10⁹⁷(98-digit number)

39873852606899247836…38037498715707718921

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

7.974 × 10⁹⁷(98-digit number)

79747705213798495672…76074997431415437839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.974 × 10⁹⁷(98-digit number)

79747705213798495672…76074997431415437841

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

1.594 × 10⁹⁸(99-digit number)

15949541042759699134…52149994862830875679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.594 × 10⁹⁸(99-digit number)

15949541042759699134…52149994862830875681

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

3.189 × 10⁹⁸(99-digit number)

31899082085519398268…04299989725661751359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.189 × 10⁹⁸(99-digit number)

31899082085519398268…04299989725661751361

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

6.379 × 10⁹⁸(99-digit number)

63798164171038796537…08599979451323502719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.379 × 10⁹⁸(99-digit number)

63798164171038796537…08599979451323502721

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

1.275 × 10⁹⁹(100-digit number)

12759632834207759307…17199958902647005439

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 #568,497

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