Block #557,408

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/22/2014, 10:22:45 PM · Difficulty 10.9629 · 6,260,368 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8473dcd36b110e7e94285fc1c63badec3d6573b5fa82ad2a7928b5d257b72235

View on Chainz ↗

Height

#557,408

Difficulty

10.962932

Transactions

Size

2.50 KB

Version

Bits

0af682af

Nonce

486,860,977

Timestamp

5/22/2014, 10:22:45 PM

Confirmations

6,260,368

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

8314737e758af98312f25ad660caa1c2bc8ab89ebe0c12feef35b5ff5cd6992b

Transactions (5)

Coinbase57b21a73b6c47b…33f5432fda9f91

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

e4fb24d15048b4…316687ec7a3536

5 in → 1 out37.3850 XPM783 B

Aa5KSvSy…DCwz8TMP

e505869fbf5355…1e4a39a411ed4d

5 in → 2 out10.2307 XPM819 B

ASUbvGQ3…eWcvX9ZX Af2BG8bg…jTCXP1FS

d7e8099d63f9ac…b18d6e31424819

1 in → 2 out2.6024 XPM227 B

AR7UGKUx…UJJe3Gnb APHx196W…DwkgXfoX

bd63c169e6c15b…377d1664bb7252

3 in → 2 out1.0368 XPM522 B

AWaNopk3…BFmXjn8p AL4RdTaL…RQtoEqnD

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.

1.064 × 10⁹⁹(100-digit number)

10649121513965301700…98148263388343531519

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

1.064 × 10⁹⁹(100-digit number)

10649121513965301700…98148263388343531519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.064 × 10⁹⁹(100-digit number)

10649121513965301700…98148263388343531521

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

2.129 × 10⁹⁹(100-digit number)

21298243027930603401…96296526776687063039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.129 × 10⁹⁹(100-digit number)

21298243027930603401…96296526776687063041

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

4.259 × 10⁹⁹(100-digit number)

42596486055861206803…92593053553374126079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.259 × 10⁹⁹(100-digit number)

42596486055861206803…92593053553374126081

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

8.519 × 10⁹⁹(100-digit number)

85192972111722413606…85186107106748252159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.519 × 10⁹⁹(100-digit number)

85192972111722413606…85186107106748252161

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

1.703 × 10¹⁰⁰(101-digit number)

17038594422344482721…70372214213496504319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.703 × 10¹⁰⁰(101-digit number)

17038594422344482721…70372214213496504321

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 #557,408

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