Block #521,074

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/2/2014, 6:19:22 AM · Difficulty 10.8606 · 6,288,843 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f6b4258e07b088243cbb85449d5e1eda681b711c9209d3de031ed7a20e1301b1

View on Chainz ↗

Height

#521,074

Difficulty

10.860646

Transactions

Size

730 B

Version

Bits

0adc5351

Nonce

30,792,528

Timestamp

5/2/2014, 6:19:22 AM

Confirmations

6,288,843

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

181b40aedc6f24cdbff872898cb243296bb2088febaa6a81f414ab5dae399efe

Transactions (2)

Coinbaseb337b3ba72c8bf…7ded412cbfab0c

1 in → 1 out8.4700 XPM116 B

AbwWkWZt…kawDhufa

74f079736a5756…54930872ad4173

3 in → 2 out7.0159 XPM522 B

ASHxq5u5…P6a3EF3E AbrzHJcs…D5FmAxSD

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.

2.673 × 10⁹⁸(99-digit number)

26730369967737266366…58266920264103919839

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

2.673 × 10⁹⁸(99-digit number)

26730369967737266366…58266920264103919839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.673 × 10⁹⁸(99-digit number)

26730369967737266366…58266920264103919841

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

5.346 × 10⁹⁸(99-digit number)

53460739935474532733…16533840528207839679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.346 × 10⁹⁸(99-digit number)

53460739935474532733…16533840528207839681

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

1.069 × 10⁹⁹(100-digit number)

10692147987094906546…33067681056415679359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.069 × 10⁹⁹(100-digit number)

10692147987094906546…33067681056415679361

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

2.138 × 10⁹⁹(100-digit number)

21384295974189813093…66135362112831358719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.138 × 10⁹⁹(100-digit number)

21384295974189813093…66135362112831358721

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

4.276 × 10⁹⁹(100-digit number)

42768591948379626186…32270724225662717439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.276 × 10⁹⁹(100-digit number)

42768591948379626186…32270724225662717441

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 #521,074

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