Block #500,605

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/19/2014, 6:13:38 AM · Difficulty 10.8012 · 6,295,015 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2528c610e3011b8357180aa71b247420f606b93bc4eccf466667bb470cd18bbb

View on Chainz ↗

Height

#500,605

Difficulty

10.801208

Transactions

Size

1.01 KB

Version

Bits

0acd1bf6

Nonce

207,176,446

Timestamp

4/19/2014, 6:13:38 AM

Confirmations

6,295,015

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3024dd54ed979d092d3d56050fad568daeaa8daa84192742962783cb127769a5

Transactions (4)

Coinbase2392c14d439c81…1e1df28f869e6c

1 in → 1 out8.5900 XPM116 B

AbwWkWZt…kawDhufa

32a12fbfb73ef9…ab7476f2cbb140

2 in → 2 out5.1431 XPM375 B

ANpJhntJ…uE39TWBu AWqJRFnX…smM7AuX3

ca2177712f467a…58ea5ddd8f9fc3

1 in → 2 out1.1733 XPM225 B

AUtJgpnk…JymhtEwE Ae3cFsa3…Gz8YRRRs

31105812dd6572…80b17cfe234cf7

1 in → 2 out2.7922 XPM226 B

AMZUX7QA…GyGfpBSs ANGJYZkp…sBJVintj

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.

3.436 × 10⁹⁸(99-digit number)

34361514522456173273…13958266087803622399

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

3.436 × 10⁹⁸(99-digit number)

34361514522456173273…13958266087803622399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.436 × 10⁹⁸(99-digit number)

34361514522456173273…13958266087803622401

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

6.872 × 10⁹⁸(99-digit number)

68723029044912346546…27916532175607244799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.872 × 10⁹⁸(99-digit number)

68723029044912346546…27916532175607244801

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

1.374 × 10⁹⁹(100-digit number)

13744605808982469309…55833064351214489599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.374 × 10⁹⁹(100-digit number)

13744605808982469309…55833064351214489601

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

2.748 × 10⁹⁹(100-digit number)

27489211617964938618…11666128702428979199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.748 × 10⁹⁹(100-digit number)

27489211617964938618…11666128702428979201

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

5.497 × 10⁹⁹(100-digit number)

54978423235929877237…23332257404857958399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.497 × 10⁹⁹(100-digit number)

54978423235929877237…23332257404857958401

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