Block #528,001

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/6/2014, 9:53:18 AM · Difficulty 10.8850 · 6,271,246 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6023669ffdb111b352a1a16a96eb7e055853b0e119c17b79cb4d0558c91cf122

View on Chainz ↗

Height

#528,001

Difficulty

10.884961

Transactions

Size

661 B

Version

Bits

0ae28cd3

Nonce

52,120,789

Timestamp

5/6/2014, 9:53:18 AM

Confirmations

6,271,246

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ec3afc77c0dd8af44e1959142c9d335a57dcf36539025833a0939dadedab3f2c

Transactions (3)

Coinbase1a3604d6ac9873…0286e3b8c6c967

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

3d38ea08db98df…5b07ec5a601cf2

1 in → 2 out79.3896 XPM226 B

AZWvNYUF…g68rodg3 AXLbkdEt…XRvVct5T

94872cda6b68a3…b6f0b847c0adf8

1 in → 2 out29.1672 XPM227 B

ATxoEAVm…o1hPnNf4 AZiuVLeH…KJD923bJ

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.

4.688 × 10⁹⁸(99-digit number)

46887008230620591290…64480073730138031739

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

4.688 × 10⁹⁸(99-digit number)

46887008230620591290…64480073730138031739

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.688 × 10⁹⁸(99-digit number)

46887008230620591290…64480073730138031741

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

9.377 × 10⁹⁸(99-digit number)

93774016461241182580…28960147460276063479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.377 × 10⁹⁸(99-digit number)

93774016461241182580…28960147460276063481

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

1.875 × 10⁹⁹(100-digit number)

18754803292248236516…57920294920552126959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.875 × 10⁹⁹(100-digit number)

18754803292248236516…57920294920552126961

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

3.750 × 10⁹⁹(100-digit number)

37509606584496473032…15840589841104253919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.750 × 10⁹⁹(100-digit number)

37509606584496473032…15840589841104253921

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

7.501 × 10⁹⁹(100-digit number)

75019213168992946064…31681179682208507839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.501 × 10⁹⁹(100-digit number)

75019213168992946064…31681179682208507841

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