Block #507,699

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 9:49:18 PM · Difficulty 10.8172 · 6,317,973 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f31d29435503beaef4ec12aeff774730151dab9c643ed099d5b3de9ab100a65b

View on Chainz ↗

Height

#507,699

Difficulty

10.817192

Transactions

Size

1.38 KB

Version

Bits

0ad13384

Nonce

18,568,050

Timestamp

4/23/2014, 9:49:18 PM

Confirmations

6,317,973

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6bd09cd9ef90156989db34617cd117c2b219e51aded68ef61ec07d2972cd659a

Transactions (5)

Coinbaseda30891bfd053a…a214549bdc3177

1 in → 1 out8.5700 XPM116 B

AbwWkWZt…kawDhufa

a685d29559e08c…a53c28e6ca831f

1 in → 2 out5.5175 XPM226 B

AcVN643J…tnTzzH2c AGXqJki6…YNiMZGMN

6343f4059244ec…71360051ad795a

1 in → 2 out4.5634 XPM226 B

AJiGJHiz…GMByTg9U AZcXqmq5…ArYvMskF

b778b8a1714f1b…cc3ee77a9fa47d

2 in → 2 out5.3180 XPM374 B

ANnbxgo4…2k5C9Uar Ae3C7vwp…qVcRwMCi

3d8c2c87a3be73…4871ee1177b4dd

2 in → 2 out1.2695 XPM375 B

AcMNnCDo…btimwL4a ATKSefYU…CJ15GUNF

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.

1.425 × 10⁹⁸(99-digit number)

14256353393152087417…33179199337853618199

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

1.425 × 10⁹⁸(99-digit number)

14256353393152087417…33179199337853618199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.425 × 10⁹⁸(99-digit number)

14256353393152087417…33179199337853618201

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

2.851 × 10⁹⁸(99-digit number)

28512706786304174834…66358398675707236399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.851 × 10⁹⁸(99-digit number)

28512706786304174834…66358398675707236401

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

5.702 × 10⁹⁸(99-digit number)

57025413572608349669…32716797351414472799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.702 × 10⁹⁸(99-digit number)

57025413572608349669…32716797351414472801

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

1.140 × 10⁹⁹(100-digit number)

11405082714521669933…65433594702828945599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.140 × 10⁹⁹(100-digit number)

11405082714521669933…65433594702828945601

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

2.281 × 10⁹⁹(100-digit number)

22810165429043339867…30867189405657891199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.281 × 10⁹⁹(100-digit number)

22810165429043339867…30867189405657891201

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

Block #507,699

Cookie Preferences