Block #300,012

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/8/2013, 8:19:34 AM · Difficulty 9.9922 · 6,506,039 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de09ab6289409c4c3da718cb0caf0a85012b6a20c522ab455b91600cebffcfac

View on Chainz ↗

Height

#300,012

Difficulty

9.992193

Transactions

Size

1.81 KB

Version

Bits

09fe0059

Nonce

49,670

Timestamp

12/8/2013, 8:19:34 AM

Confirmations

6,506,039

Mined by

⛏️ aR,`AZ2pPuKgN7GXPJPBLxtm9bkWcE95SN2Yr7

Merkle Root

9f3f329640491794bd9bff1067872d86feabb733504b3a936fd5799d140a075d

Transactions (4)

Coinbase447a29a46109e1…6b3c7beaa18940

1 in → 30 out9.9800 XPM1.06 KB

AZ2pPuKg…95SN2Yr7 ARy21REr…6pBWtQJ2 AJzWx2VD…j4ZSMit5 ANqCLxyk…2yVxwxBy AQf7sjuh…sNY5fXpu

9187712e966cd9…9fa0020a4ffdf8

1 in → 2 out3858.1047 XPM226 B

APKQjCVG…KgFWRKZW AThwcFQf…7B7U8wG4

37ffd31322b4dc…93245df44d6ffb

1 in → 2 out303.9276 XPM227 B

AUFX4uz2…EwXuc5GT AL9gcRfF…PJgN6kpB

f298127def5356…ec1b2a896b3586

1 in → 2 out298.8551 XPM225 B

ARaJvMsj…1JLDboxK AQj5KawP…ApHesLav

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.

5.147 × 10⁸⁸(89-digit number)

51475039553432313476…25211089452265298559

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

5.147 × 10⁸⁸(89-digit number)

51475039553432313476…25211089452265298559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.147 × 10⁸⁸(89-digit number)

51475039553432313476…25211089452265298561

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

1.029 × 10⁸⁹(90-digit number)

10295007910686462695…50422178904530597119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.029 × 10⁸⁹(90-digit number)

10295007910686462695…50422178904530597121

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

2.059 × 10⁸⁹(90-digit number)

20590015821372925390…00844357809061194239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.059 × 10⁸⁹(90-digit number)

20590015821372925390…00844357809061194241

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

4.118 × 10⁸⁹(90-digit number)

41180031642745850781…01688715618122388479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.118 × 10⁸⁹(90-digit number)

41180031642745850781…01688715618122388481

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

8.236 × 10⁸⁹(90-digit number)

82360063285491701562…03377431236244776959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.236 × 10⁸⁹(90-digit number)

82360063285491701562…03377431236244776961

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