Block #526,925

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/5/2014, 4:54:13 PM · Difficulty 10.8837 · 6,285,652 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ec1f7753e73cae6f9ac8825a3f38c9e942a6c56de00fceefd298e797cc40fbf

View on Chainz ↗

Height

#526,925

Difficulty

10.883691

Transactions

Size

957 B

Version

Bits

0ae23990

Nonce

266,038

Timestamp

5/5/2014, 4:54:13 PM

Confirmations

6,285,652

Mined by

⛏️ MAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

587933cdc886ad28948c0368cc1d0dcf8a94ab0458b9b4120f977bfaea697a70

Transactions (2)

Coinbasec4bc4675e614f1…dae08a199da72a

1 in → 17 out8.4300 XPM641 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j

201ac9c984be78…97237c7258da72

1 in → 2 out3.7066 XPM226 B

AM8GuxnN…AfjbhWoV AHUFJbHW…aZ5jmy6T

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.

1.657 × 10⁹⁴(95-digit number)

16578875104036752705…62965674003709687039

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

1.657 × 10⁹⁴(95-digit number)

16578875104036752705…62965674003709687039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.657 × 10⁹⁴(95-digit number)

16578875104036752705…62965674003709687041

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

3.315 × 10⁹⁴(95-digit number)

33157750208073505411…25931348007419374079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.315 × 10⁹⁴(95-digit number)

33157750208073505411…25931348007419374081

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

6.631 × 10⁹⁴(95-digit number)

66315500416147010823…51862696014838748159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.631 × 10⁹⁴(95-digit number)

66315500416147010823…51862696014838748161

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

1.326 × 10⁹⁵(96-digit number)

13263100083229402164…03725392029677496319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.326 × 10⁹⁵(96-digit number)

13263100083229402164…03725392029677496321

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

2.652 × 10⁹⁵(96-digit number)

26526200166458804329…07450784059354992639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.652 × 10⁹⁵(96-digit number)

26526200166458804329…07450784059354992641

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 #526,925

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