Block #507,417

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 5:37:14 PM · Difficulty 10.8161 · 6,299,793 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9160a9956bc99d2e28c207cbc8e1c193d4a80cc487b90d3f701b501f30e70bfb

View on Chainz ↗

Height

#507,417

Difficulty

10.816103

Transactions

Size

764 B

Version

Bits

0ad0ec1e

Nonce

114,611

Timestamp

4/23/2014, 5:37:14 PM

Confirmations

6,299,793

Mined by

AREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

09e3b012d1b93ffacddfd23dd32e6c5b22dea872be91d326127c2c3ce6aa65c3

Transactions (1)

Coinbase09e3b012d1b93f…7c2c3ce6aa65c3

1 in → 18 out8.5300 XPM675 B

AREQGaCC…V47D9Shh AUzEPJFG…kYkA5U9V ATp4jJhs…TbSgR8Qb AGz9gyZW…bo8NYQpw AWFABhGb…QWK99PRN

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.

2.000 × 10⁹²(93-digit number)

20004707703681967296…88766065050935288319

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

2.000 × 10⁹²(93-digit number)

20004707703681967296…88766065050935288319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.000 × 10⁹²(93-digit number)

20004707703681967296…88766065050935288321

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

4.000 × 10⁹²(93-digit number)

40009415407363934593…77532130101870576639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.000 × 10⁹²(93-digit number)

40009415407363934593…77532130101870576641

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

8.001 × 10⁹²(93-digit number)

80018830814727869186…55064260203741153279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.001 × 10⁹²(93-digit number)

80018830814727869186…55064260203741153281

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

1.600 × 10⁹³(94-digit number)

16003766162945573837…10128520407482306559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.600 × 10⁹³(94-digit number)

16003766162945573837…10128520407482306561

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

3.200 × 10⁹³(94-digit number)

32007532325891147674…20257040814964613119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.200 × 10⁹³(94-digit number)

32007532325891147674…20257040814964613121

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 #507,417

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