Block #571,060

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/1/2014, 5:57:25 AM · Difficulty 10.9651 · 6,245,267 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

07c0ae240ae68c38c89c96386d156219298273724be8468e81f9ece1139ddcf4

View on Chainz ↗

Height

#571,060

Difficulty

10.965070

Transactions

Size

1.59 KB

Version

Bits

0af70eda

Nonce

212,049,508

Timestamp

6/1/2014, 5:57:25 AM

Confirmations

6,245,267

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

086621d6f2d2211b5dcea4796c1a57e217413cb854af6987373f09718b0d36bb

Transactions (4)

Coinbaseab26c2819a9a6b…8a2fce45fd1194

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

234bae1d66269c…ca5c438b0efe12

1 in → 2 out8.2900 XPM225 B

AXu8B3yL…5g33w9LG Ad2ufdss…FpRKN6iP

bdd6388623ffa0…7741254cb1650b

4 in → 2 out31.4718 XPM672 B

AMot5PR7…5gRdK6NM AY9hyv36…C9eENgsU

5c910b59f72952…3fdb657ddf8cfe

3 in → 2 out20.9372 XPM522 B

AS8xEwRt…HruqFt23 AG33QRe9…Dfo3iZ3N

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.

1.532 × 10⁹⁷(98-digit number)

15320593501028700068…96461825761240235599

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

1.532 × 10⁹⁷(98-digit number)

15320593501028700068…96461825761240235599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.532 × 10⁹⁷(98-digit number)

15320593501028700068…96461825761240235601

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

3.064 × 10⁹⁷(98-digit number)

30641187002057400136…92923651522480471199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.064 × 10⁹⁷(98-digit number)

30641187002057400136…92923651522480471201

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

6.128 × 10⁹⁷(98-digit number)

61282374004114800272…85847303044960942399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.128 × 10⁹⁷(98-digit number)

61282374004114800272…85847303044960942401

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

1.225 × 10⁹⁸(99-digit number)

12256474800822960054…71694606089921884799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.225 × 10⁹⁸(99-digit number)

12256474800822960054…71694606089921884801

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

2.451 × 10⁹⁸(99-digit number)

24512949601645920108…43389212179843769599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.451 × 10⁹⁸(99-digit number)

24512949601645920108…43389212179843769601

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 #571,060

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