Block #518,134

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2014, 10:00:34 AM · Difficulty 10.8525 · 6,284,363 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ed26f40d3f29ee295f507471c10e1b2e033b966505e0eda976c9e5ca9a3a6de1

View on Chainz ↗

Height

#518,134

Difficulty

10.852509

Transactions

Size

1.69 KB

Version

Bits

0ada3e0b

Nonce

20,937

Timestamp

4/30/2014, 10:00:34 AM

Confirmations

6,284,363

Mined by

AGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

1d5dc2391f73a9a3472436bbd53678139b43a0042dfc4bdceb2a09e80696ddc6

Transactions (4)

Coinbasebbdc66d77173df…aa1aa5c799013e

1 in → 22 out8.5100 XPM811 B

AGz9gyZW…bo8NYQpw AMVf7Jrg…xd5AVR7C AMW1p9oT…2TzdaZxH AUzEPJFG…kYkA5U9V AUFKXvnz…342ApNcm

5ca391b37ddbd6…4158252d046068

2 in → 2 out3.0646 XPM373 B

AeVqj1UG…5QGSYuvW ASG3uRNW…E5fEZ9H7

678fd96d2a2cea…75730b5b767e2b

1 in → 2 out1.8081 XPM227 B

AQQ2Uy1H…BxBHXtQW AWEm1NVx…BSyUpTdF

d88ac6d99faf6f…5e3c3003c015fc

1 in → 2 out2.2998 XPM226 B

ARBo3mrR…ChB1pPoQ AKnCLhwV…heu59RZv

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.

4.326 × 10¹¹⁰(111-digit number)

43267279960280435783…79765691960281863679

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

4.326 × 10¹¹⁰(111-digit number)

43267279960280435783…79765691960281863679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.326 × 10¹¹⁰(111-digit number)

43267279960280435783…79765691960281863681

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

8.653 × 10¹¹⁰(111-digit number)

86534559920560871566…59531383920563727359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.653 × 10¹¹⁰(111-digit number)

86534559920560871566…59531383920563727361

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

1.730 × 10¹¹¹(112-digit number)

17306911984112174313…19062767841127454719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.730 × 10¹¹¹(112-digit number)

17306911984112174313…19062767841127454721

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

3.461 × 10¹¹¹(112-digit number)

34613823968224348626…38125535682254909439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.461 × 10¹¹¹(112-digit number)

34613823968224348626…38125535682254909441

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

6.922 × 10¹¹¹(112-digit number)

69227647936448697253…76251071364509818879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.922 × 10¹¹¹(112-digit number)

69227647936448697253…76251071364509818881

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