Block #509,528

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/25/2014, 3:01:11 AM · Difficulty 10.8200 · 6,301,541 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d897e944f1b299336549b89ecfa84418c2dd1c4d3089bcd73d041f26720bca3

View on Chainz ↗

Height

#509,528

Difficulty

10.820030

Transactions

Size

1020 B

Version

Bits

0ad1ed79

Nonce

201,444

Timestamp

4/25/2014, 3:01:11 AM

Confirmations

6,301,541

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

2e19d3e2a7cabc18a7aa01d8e5d96e6f4b4a3261ae3bccb6a7f18b183663c605

Transactions (2)

Coinbase2edb4fbeafb178…eeb450dc65f432

1 in → 1 out8.5500 XPM110 B

AeKNrjNj…1NEq95Ta

0875a82486ba53…e940f6200c396c

5 in → 2 out158.1958 XPM819 B

AVSYbYBW…vk3vhxwZ AHdBX7gj…ksiEMFEu

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.

7.299 × 10⁹⁷(98-digit number)

72999526796484132123…38963566965535843039

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

7.299 × 10⁹⁷(98-digit number)

72999526796484132123…38963566965535843039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.299 × 10⁹⁷(98-digit number)

72999526796484132123…38963566965535843041

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

1.459 × 10⁹⁸(99-digit number)

14599905359296826424…77927133931071686079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.459 × 10⁹⁸(99-digit number)

14599905359296826424…77927133931071686081

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

2.919 × 10⁹⁸(99-digit number)

29199810718593652849…55854267862143372159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.919 × 10⁹⁸(99-digit number)

29199810718593652849…55854267862143372161

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

5.839 × 10⁹⁸(99-digit number)

58399621437187305698…11708535724286744319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.839 × 10⁹⁸(99-digit number)

58399621437187305698…11708535724286744321

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

1.167 × 10⁹⁹(100-digit number)

11679924287437461139…23417071448573488639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.167 × 10⁹⁹(100-digit number)

11679924287437461139…23417071448573488641

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 #509,528

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