Block #500,462

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/19/2014, 4:15:48 AM · Difficulty 10.8002 · 6,309,356 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

15b09b7df854e120bd0cfe6bd4cf6a50d4f26987a3084ce89ce758fa01b97d52

View on Chainz ↗

Height

#500,462

Difficulty

10.800231

Transactions

Size

1.57 KB

Version

Bits

0accdbf5

Nonce

32,973,179

Timestamp

4/19/2014, 4:15:48 AM

Confirmations

6,309,356

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

9216451df94cf6ad7533f91524d00e928f68b8e2a909f4bd17c345b250fdce94

Transactions (4)

Coinbase34419aa895529c…9b3894c836f866

1 in → 1 out8.5900 XPM116 B

AbwWkWZt…kawDhufa

231be1c9ddd257…c7873a6345fa3c

3 in → 9 out25.9800 XPM659 B

AW7MfWAo…caab44fx AcBnBiUw…CYFN81QZ AeKNrjNj…1NEq95Ta AU8K9zCe…2NaCayba AQgZKPra…nwpjY1Ad

de748a8b41e38e…862b55d14d6371

1 in → 2 out0.7013 XPM226 B

AeHmxERP…2hhYf2ho AMWbccC9…UAr3YG81

e6a9b3aaeda6bf…9e585fb932f653

3 in → 2 out0.5574 XPM520 B

AGbcRPsW…mwiEHJMF AUEfgciq…JxYNG9Ty

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.

1.122 × 10⁹⁸(99-digit number)

11224124726249678981…24593723773135168959

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

1.122 × 10⁹⁸(99-digit number)

11224124726249678981…24593723773135168959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.122 × 10⁹⁸(99-digit number)

11224124726249678981…24593723773135168961

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

2.244 × 10⁹⁸(99-digit number)

22448249452499357963…49187447546270337919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.244 × 10⁹⁸(99-digit number)

22448249452499357963…49187447546270337921

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

4.489 × 10⁹⁸(99-digit number)

44896498904998715927…98374895092540675839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.489 × 10⁹⁸(99-digit number)

44896498904998715927…98374895092540675841

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

8.979 × 10⁹⁸(99-digit number)

89792997809997431854…96749790185081351679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.979 × 10⁹⁸(99-digit number)

89792997809997431854…96749790185081351681

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

1.795 × 10⁹⁹(100-digit number)

17958599561999486370…93499580370162703359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.795 × 10⁹⁹(100-digit number)

17958599561999486370…93499580370162703361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.591 × 10⁹⁹(100-digit number)

35917199123998972741…86999160740325406719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #500,462

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