Block #2,812,143

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/27/2018, 11:46:46 AM · Difficulty 11.6687 · 4,020,640 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f7ca64893c870ebeb9cfdc3a7db743c80def29d909740d90970683755e38e31f

View on Chainz ↗

Height

#2,812,143

Difficulty

11.668733

Transactions

Size

1.88 KB

Version

Bits

0bab3210

Nonce

2,037,605,631

Timestamp

8/27/2018, 11:46:46 AM

Confirmations

4,020,640

Mined by

⛏️ P2SHALQGpaT6bUeDR1X73XRmMe4Z6w9dLVU1B9

Merkle Root

f385059a3ea2ca57a3e4b23d38b21c43866a77f3346b952b9c84d7be0f1193e1

Transactions (5)

Coinbase337f732d94c7f3…d0d2ee6ee9b602

1 in → 1 out7.3700 XPM109 B

ALQGpaT6…9dLVU1B9

ca64065f6e72d7…968408346060c5

1 in → 2 out7.3200 XPM193 B

AJ3vLnyy…V4s4jbf9 AYny1ZKx…nmyLGavN

f4653430de8d87…fcd7007c3fa7a0

2 in → 2 out10.6290 XPM340 B

AGzrd4MM…7HC9qVLn AQSMG9n1…9rZEcWQ8

89a2e0f489b1d7…950988e728be2a

2 in → 2 out5.4657 XPM374 B

AXCGoVa4…4e7qSiHM AN9v2YHG…rvePpetx

abc313cdca4d27…8494d0ee71a6c1

5 in → 2 out1.0160 XPM818 B

AZVQxXJx…o5bk74m2 AK8dDdZY…tiH1UZ7n

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.

5.062 × 10⁹⁴(95-digit number)

50621228460310439246…37204790435749975359

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

5.062 × 10⁹⁴(95-digit number)

50621228460310439246…37204790435749975359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.062 × 10⁹⁴(95-digit number)

50621228460310439246…37204790435749975361

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

1.012 × 10⁹⁵(96-digit number)

10124245692062087849…74409580871499950719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.012 × 10⁹⁵(96-digit number)

10124245692062087849…74409580871499950721

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

2.024 × 10⁹⁵(96-digit number)

20248491384124175698…48819161742999901439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.024 × 10⁹⁵(96-digit number)

20248491384124175698…48819161742999901441

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

4.049 × 10⁹⁵(96-digit number)

40496982768248351397…97638323485999802879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.049 × 10⁹⁵(96-digit number)

40496982768248351397…97638323485999802881

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

8.099 × 10⁹⁵(96-digit number)

80993965536496702794…95276646971999605759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.099 × 10⁹⁵(96-digit number)

80993965536496702794…95276646971999605761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.619 × 10⁹⁶(97-digit number)

16198793107299340558…90553293943999211519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,812,143

Cookie Preferences