Block #456,518

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/23/2014, 7:08:21 AM · Difficulty 10.4154 · 6,370,564 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0fe5633698c37be8bbc25da19c97e23bfeb7c819f8fb05ee2d96c117a73f9183

View on Chainz ↗

Height

#456,518

Difficulty

10.415417

Transactions

Size

879 B

Version

Bits

0a6a58bf

Nonce

64,039

Timestamp

3/23/2014, 7:08:21 AM

Confirmations

6,370,564

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f4cb3002cab8b6398a0b3850ff2b94f0c4ad02885bb1b0952e21b3b6358da402

Transactions (4)

Coinbasea622526bf7a6b5…6e212be2e8b96d

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

6b9cccd2490857…169eea9779edfc

1 in → 2 out6.1780 XPM226 B

AHnGsxTu…GhZYCSzj ASgRkh3b…nkavG8hW

abd2d5e946577c…20ce7ffb0d1a82

1 in → 2 out3.1626 XPM225 B

AMWhfZow…EH5vsb34 Ad5wSS1Q…qh5aoeT9

4598f072eafc6b…1d71b62a5711e5

1 in → 2 out6.1639 XPM226 B

ASgJoQeY…CL8FdgEK AMNoS32S…niT5aQFA

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.

1.033 × 10⁹⁹(100-digit number)

10335070720064537429…98928636073372876799

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

1.033 × 10⁹⁹(100-digit number)

10335070720064537429…98928636073372876799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.033 × 10⁹⁹(100-digit number)

10335070720064537429…98928636073372876801

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

2.067 × 10⁹⁹(100-digit number)

20670141440129074859…97857272146745753599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.067 × 10⁹⁹(100-digit number)

20670141440129074859…97857272146745753601

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

4.134 × 10⁹⁹(100-digit number)

41340282880258149719…95714544293491507199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.134 × 10⁹⁹(100-digit number)

41340282880258149719…95714544293491507201

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

8.268 × 10⁹⁹(100-digit number)

82680565760516299438…91429088586983014399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.268 × 10⁹⁹(100-digit number)

82680565760516299438…91429088586983014401

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

1.653 × 10¹⁰⁰(101-digit number)

16536113152103259887…82858177173966028799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.653 × 10¹⁰⁰(101-digit number)

16536113152103259887…82858177173966028801

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 #456,518

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