Block #452,020

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 8:09:02 AM · Difficulty 10.3839 · 6,356,061 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b690e8c9bc5130d87313c13c881307109bc4480ca880b83e341b623993c36d9

View on Chainz ↗

Height

#452,020

Difficulty

10.383923

Transactions

Size

2.13 KB

Version

Bits

0a6248cf

Nonce

29,510

Timestamp

3/20/2014, 8:09:02 AM

Confirmations

6,356,061

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

f899c55d23284842eded67d353ad6630c92e4b936e6e025920da4aa9b122be94

Transactions (5)

Coinbase96a3bb9b136051…70565011fcacd2

1 in → 1 out9.3100 XPM110 B

AeKNrjNj…1NEq95Ta

54ea11bcb98800…3d22454f2d8c7c

6 in → 18 out55.7900 XPM1.27 KB

Ac1R3z63…az1K8bt3 AeKNrjNj…1NEq95Ta AcrLeg9u…hFnsjy5L ARLVb39P…bhtXdkU3 AWCifDd1…Nv6sojqc

73cae3f5bb831e…54938a115b79df

1 in → 2 out7.2370 XPM226 B

APFvqWhD…ugh83MuL Ab7KvdoN…BMF3E7hn

ca14645c6dd7d2…ef8ae289f41cf9

1 in → 2 out7.1982 XPM227 B

ATkcN1Jp…QxiwhsrR AVYWpamp…3Xtz41QK

ae263f0736c026…8728e4bd8c6205

1 in → 2 out4.6550 XPM227 B

AatWZbeD…icfV8WtX AHvJbmvX…CcHR6woV

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.

1.856 × 10¹⁰¹(102-digit number)

18565224920601199798…91482175199302556299

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

1.856 × 10¹⁰¹(102-digit number)

18565224920601199798…91482175199302556299

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.856 × 10¹⁰¹(102-digit number)

18565224920601199798…91482175199302556301

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

3.713 × 10¹⁰¹(102-digit number)

37130449841202399596…82964350398605112599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.713 × 10¹⁰¹(102-digit number)

37130449841202399596…82964350398605112601

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

7.426 × 10¹⁰¹(102-digit number)

74260899682404799192…65928700797210225199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.426 × 10¹⁰¹(102-digit number)

74260899682404799192…65928700797210225201

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

1.485 × 10¹⁰²(103-digit number)

14852179936480959838…31857401594420450399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.485 × 10¹⁰²(103-digit number)

14852179936480959838…31857401594420450401

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

2.970 × 10¹⁰²(103-digit number)

29704359872961919676…63714803188840900799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.970 × 10¹⁰²(103-digit number)

29704359872961919676…63714803188840900801

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 #452,020

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