Block #519,828

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/1/2014, 11:36:18 AM · Difficulty 10.8572 · 6,296,470 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cef7a746de168633443cb561752019be8266a7d0e7e9d98c3d6949cdd9e3a0ce

View on Chainz ↗

Height

#519,828

Difficulty

10.857150

Transactions

Size

991 B

Version

Bits

0adb6e2f

Nonce

27,512,923

Timestamp

5/1/2014, 11:36:18 AM

Confirmations

6,296,470

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

8069929a9c4ecec346844afaa26564c1bcdc190db85526ac648aea95fb53bc7c

Transactions (3)

Coinbase734f91fe8a1287…0ba2ffbdf89f1a

1 in → 1 out8.4900 XPM116 B

AbwWkWZt…kawDhufa

bd7b6b8e2815ab…ca5aeba6a3cbb3

3 in → 3 out7.2609 XPM556 B

AWa3SoPq…pzpXymrR AHXJ1dhk…mhL46N6m AeKNrjNj…1NEq95Ta

246f555d3fb909…b3271ea318f066

1 in → 2 out5.9309 XPM227 B

AZT5cEAj…KfQcV1uS ASUbvGQ3…eWcvX9ZX

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.

6.449 × 10⁹⁹(100-digit number)

64499710908625035345…78704992357701165119

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

6.449 × 10⁹⁹(100-digit number)

64499710908625035345…78704992357701165119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.449 × 10⁹⁹(100-digit number)

64499710908625035345…78704992357701165121

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

1.289 × 10¹⁰⁰(101-digit number)

12899942181725007069…57409984715402330239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.289 × 10¹⁰⁰(101-digit number)

12899942181725007069…57409984715402330241

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

2.579 × 10¹⁰⁰(101-digit number)

25799884363450014138…14819969430804660479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.579 × 10¹⁰⁰(101-digit number)

25799884363450014138…14819969430804660481

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

5.159 × 10¹⁰⁰(101-digit number)

51599768726900028276…29639938861609320959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.159 × 10¹⁰⁰(101-digit number)

51599768726900028276…29639938861609320961

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

1.031 × 10¹⁰¹(102-digit number)

10319953745380005655…59279877723218641919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.031 × 10¹⁰¹(102-digit number)

10319953745380005655…59279877723218641921

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 #519,828

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