Block #472,190

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/3/2014, 2:56:53 AM · Difficulty 10.4338 · 6,320,423 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1a70e3c872c2c66384d972a18dd5ab278c827582d2fe6ee7d3fbfd29f7b07269

View on Chainz ↗

Height

#472,190

Difficulty

10.433805

Transactions

Size

1.99 KB

Version

Bits

0a6f0ddf

Nonce

181,477

Timestamp

4/3/2014, 2:56:53 AM

Confirmations

6,320,423

Merkle Root

60578b0dd64bc52a5c8985cbfa2a1e861771f001999daa39dbdc9177dfa3bd4e

Transactions (4)

Coinbase43b744b2b1cc1d…f56d23ab2adbac

1 in → 1 out9.2100 XPM109 B

AeBQu5Ue…MYbzxpgo

0d950702ae75fa…c6b2e24c4d0b72

5 in → 15 out45.9000 XPM1.06 KB

AK6P7xdW…xLXseJWb AN3RbycA…MtRVWB2n AJvKq8HD…WqkH2BmK AeKNrjNj…1NEq95Ta AWQhak32…eArVqMxc

e547d2418c7915…f9741888980531

3 in → 2 out4.1019 XPM521 B

APf8oqq4…oYGVopsw AJbxxT8R…gBxqX66F

5d1961fa308612…b2d5c57b67170e

1 in → 2 out1.5415 XPM226 B

AcdyemUU…wyL11368 AGHJgHmJ…xarHBeuW

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.

7.745 × 10⁹⁶(97-digit number)

77456899260673011320…61528189907424151439

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

7.745 × 10⁹⁶(97-digit number)

77456899260673011320…61528189907424151439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.745 × 10⁹⁶(97-digit number)

77456899260673011320…61528189907424151441

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

1.549 × 10⁹⁷(98-digit number)

15491379852134602264…23056379814848302879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.549 × 10⁹⁷(98-digit number)

15491379852134602264…23056379814848302881

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

3.098 × 10⁹⁷(98-digit number)

30982759704269204528…46112759629696605759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.098 × 10⁹⁷(98-digit number)

30982759704269204528…46112759629696605761

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

6.196 × 10⁹⁷(98-digit number)

61965519408538409056…92225519259393211519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.196 × 10⁹⁷(98-digit number)

61965519408538409056…92225519259393211521

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

1.239 × 10⁹⁸(99-digit number)

12393103881707681811…84451038518786423039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.239 × 10⁹⁸(99-digit number)

12393103881707681811…84451038518786423041

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