Block #519,438

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/1/2014, 5:42:50 AM · Difficulty 10.8561 · 6,289,417 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dee08aa5f6835d24df0880715fbf0cf2a06a32b8bd6b252f85ae32c3a84c0979

View on Chainz ↗

Height

#519,438

Difficulty

10.856068

Transactions

Size

1.01 KB

Version

Bits

0adb2747

Nonce

9,890,198

Timestamp

5/1/2014, 5:42:50 AM

Confirmations

6,289,417

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

210acbe02805d874e7968d34111f77acad79cc75eaa1554ddf3b32f38bdedefd

Transactions (4)

Coinbaseae9ca6948f3a50…a5e7ca2659e24e

1 in → 1 out8.5000 XPM116 B

AbwWkWZt…kawDhufa

cff23a9ece1f3b…64c1a9612549a3

2 in → 2 out17.0400 XPM375 B

AY2MMHQo…FPQjgQGx AanKg56N…aJurLR3D

5ac5d5c0aae03d…974045ea6ee047

1 in → 2 out8.4800 XPM227 B

AMGeeEpe…bLcrvDaS AG8u7ddV…cU5QJSqk

19b2a91b6025f4…e11a3111cd97c4

1 in → 2 out3.4021 XPM225 B

AK6ZxWYZ…CoC1om7m AH7Jv3Bm…xoeobmRq

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.

8.595 × 10¹⁰⁰(101-digit number)

85959316145007337216…28560942633931898879

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

8.595 × 10¹⁰⁰(101-digit number)

85959316145007337216…28560942633931898879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.595 × 10¹⁰⁰(101-digit number)

85959316145007337216…28560942633931898881

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

1.719 × 10¹⁰¹(102-digit number)

17191863229001467443…57121885267863797759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.719 × 10¹⁰¹(102-digit number)

17191863229001467443…57121885267863797761

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

3.438 × 10¹⁰¹(102-digit number)

34383726458002934886…14243770535727595519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.438 × 10¹⁰¹(102-digit number)

34383726458002934886…14243770535727595521

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

6.876 × 10¹⁰¹(102-digit number)

68767452916005869773…28487541071455191039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.876 × 10¹⁰¹(102-digit number)

68767452916005869773…28487541071455191041

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

1.375 × 10¹⁰²(103-digit number)

13753490583201173954…56975082142910382079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.375 × 10¹⁰²(103-digit number)

13753490583201173954…56975082142910382081

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 #519,438

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