Block #531,573

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/8/2014, 2:20:55 PM · Difficulty 10.8945 · 6,273,437 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1acc743d8c6e24f8b8dfb19908d2501709a73cf7cdf12a01b1df0933f605b05

View on Chainz ↗

Height

#531,573

Difficulty

10.894502

Transactions

Size

697 B

Version

Bits

0ae4fe16

Nonce

319,083

Timestamp

5/8/2014, 2:20:55 PM

Confirmations

6,273,437

Mined by

⛏️ uaSksAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

a07b354ff4104deb2f91ba80313c50e7d2fb1e08efac8c0e72f5409feea740b1

Transactions (1)

Coinbasea07b354ff4104d…f5409feea740b1

1 in → 16 out8.4030 XPM607 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn

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.

1.399 × 10⁹⁵(96-digit number)

13994096169274186332…85038265249520574159

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

1.399 × 10⁹⁵(96-digit number)

13994096169274186332…85038265249520574159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.399 × 10⁹⁵(96-digit number)

13994096169274186332…85038265249520574161

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

2.798 × 10⁹⁵(96-digit number)

27988192338548372665…70076530499041148319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.798 × 10⁹⁵(96-digit number)

27988192338548372665…70076530499041148321

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

5.597 × 10⁹⁵(96-digit number)

55976384677096745331…40153060998082296639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.597 × 10⁹⁵(96-digit number)

55976384677096745331…40153060998082296641

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

1.119 × 10⁹⁶(97-digit number)

11195276935419349066…80306121996164593279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.119 × 10⁹⁶(97-digit number)

11195276935419349066…80306121996164593281

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

2.239 × 10⁹⁶(97-digit number)

22390553870838698132…60612243992329186559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.239 × 10⁹⁶(97-digit number)

22390553870838698132…60612243992329186561

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