Block #511,957

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/26/2014, 2:01:12 PM · Difficulty 10.8315 · 6,281,818 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2ad4a9d15219f3c077907591f7e9ecf3ad60bbf24b6a1a10eab4b45becbf56cb

View on Chainz ↗

Height

#511,957

Difficulty

10.831547

Transactions

Size

696 B

Version

Bits

0ad4e03f

Nonce

205,506

Timestamp

4/26/2014, 2:01:12 PM

Confirmations

6,281,818

Merkle Root

b3b14fc5f0b4a5ae020143ef5d4054db67488182f3f6da3a5ecabc2ba24fc6a8

Transactions (1)

Coinbaseb3b14fc5f0b4a5…cabc2ba24fc6a8

1 in → 16 out8.5100 XPM607 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j

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.

8.335 × 10⁹¹(92-digit number)

83353064178768530469…54622130862368417249

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

8.335 × 10⁹¹(92-digit number)

83353064178768530469…54622130862368417249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.335 × 10⁹¹(92-digit number)

83353064178768530469…54622130862368417251

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

1.667 × 10⁹²(93-digit number)

16670612835753706093…09244261724736834499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.667 × 10⁹²(93-digit number)

16670612835753706093…09244261724736834501

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

3.334 × 10⁹²(93-digit number)

33341225671507412187…18488523449473668999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.334 × 10⁹²(93-digit number)

33341225671507412187…18488523449473669001

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

6.668 × 10⁹²(93-digit number)

66682451343014824375…36977046898947337999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.668 × 10⁹²(93-digit number)

66682451343014824375…36977046898947338001

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

1.333 × 10⁹³(94-digit number)

13336490268602964875…73954093797894675999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.333 × 10⁹³(94-digit number)

13336490268602964875…73954093797894676001

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