Block #573,706

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/2/2014, 9:13:54 PM · Difficulty 10.9671 · 6,235,369 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

172fcd48d9f952bbebc6f1dfb5082ef9babc5da22fc950c3adcb025f3f12cba5

View on Chainz ↗

Height

#573,706

Difficulty

10.967103

Transactions

Size

954 B

Version

Bits

0af79410

Nonce

644,972,528

Timestamp

6/2/2014, 9:13:54 PM

Confirmations

6,235,369

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

fe42ba10ae8dd8ff9c491d204fd85dbf51efc132b604f576b1dfca7062f5ef62

Transactions (3)

Coinbase9c1bb9fa729f81…bfd3ca81bf46b3

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

30cc53387f4479…ce2b7230c9d1b1

1 in → 2 out5.2020 XPM225 B

AZPkERnZ…2xA7tiAH AcdyemUU…wyL11368

d559abaf6b9b6d…7d31de053de650

3 in → 2 out1.0689 XPM522 B

AdyKqw36…tD6o6LjL Abs1CTRR…uk6ieBYF

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.

2.246 × 10⁹⁸(99-digit number)

22469183566682631168…35495391383660374079

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

2.246 × 10⁹⁸(99-digit number)

22469183566682631168…35495391383660374079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.246 × 10⁹⁸(99-digit number)

22469183566682631168…35495391383660374081

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

4.493 × 10⁹⁸(99-digit number)

44938367133365262337…70990782767320748159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.493 × 10⁹⁸(99-digit number)

44938367133365262337…70990782767320748161

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

8.987 × 10⁹⁸(99-digit number)

89876734266730524674…41981565534641496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.987 × 10⁹⁸(99-digit number)

89876734266730524674…41981565534641496321

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

1.797 × 10⁹⁹(100-digit number)

17975346853346104934…83963131069282992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.797 × 10⁹⁹(100-digit number)

17975346853346104934…83963131069282992641

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

3.595 × 10⁹⁹(100-digit number)

35950693706692209869…67926262138565985279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.595 × 10⁹⁹(100-digit number)

35950693706692209869…67926262138565985281

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 #573,706

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