Block #453,845

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/21/2014, 1:35:22 PM · Difficulty 10.3918 · 6,352,552 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cc0c5a7047b8a5a0e509bef6f4daba36c927a35270ea04e6625f6d3bd5cc0202

View on Chainz ↗

Height

#453,845

Difficulty

10.391760

Transactions

Size

1.06 KB

Version

Bits

0a644a5e

Nonce

10,517

Timestamp

3/21/2014, 1:35:22 PM

Confirmations

6,352,552

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

64232dc4e984013007633992f5845d46005267892401e63dd94a0593b90fda2c

Transactions (2)

Coinbase97ff5137b96813…3f095d56bdabf0

1 in → 1 out9.2600 XPM116 B

AbwWkWZt…kawDhufa

c303cb751bcd2d…e19c2287e1443c

4 in → 12 out37.1100 XPM873 B

AcPHTmqg…WJtAX8A1 AL5wNHbW…dFU2npvz APGhKKy1…axmZARuS AU6HwChT…Sp2NiXRS AHAPmauK…a5LvR1Xp

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.

1.237 × 10¹⁰³(104-digit number)

12378325788588873611…50454654126055751679

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

1.237 × 10¹⁰³(104-digit number)

12378325788588873611…50454654126055751679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.237 × 10¹⁰³(104-digit number)

12378325788588873611…50454654126055751681

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

2.475 × 10¹⁰³(104-digit number)

24756651577177747223…00909308252111503359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.475 × 10¹⁰³(104-digit number)

24756651577177747223…00909308252111503361

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

4.951 × 10¹⁰³(104-digit number)

49513303154355494446…01818616504223006719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.951 × 10¹⁰³(104-digit number)

49513303154355494446…01818616504223006721

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

9.902 × 10¹⁰³(104-digit number)

99026606308710988892…03637233008446013439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.902 × 10¹⁰³(104-digit number)

99026606308710988892…03637233008446013441

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

1.980 × 10¹⁰⁴(105-digit number)

19805321261742197778…07274466016892026879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.980 × 10¹⁰⁴(105-digit number)

19805321261742197778…07274466016892026881

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 #453,845

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