Block #2,872,302

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/8/2018, 7:43:52 AM · Difficulty 11.6659 · 3,965,479 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ab39c5170a06139d89d187f02a8d95cd2fbad4239b6faef33637d85b156a339f

View on Chainz ↗

Height

#2,872,302

Difficulty

11.665871

Transactions

Size

2.30 KB

Version

Bits

0baa7688

Nonce

389,429,866

Timestamp

10/8/2018, 7:43:52 AM

Confirmations

3,965,479

Mined by

⛏️ P2SHAVdK4q4BZvBgjtUYAxtJq4PfjiqKzkY1qs

Merkle Root

c4f9c1d607fa178b9edec9a25ed61acc65e84e94e4b1f8af71ebb110116cd9ac

Transactions (2)

Coinbase1d1e8073bf7152…ebad1929143d66

1 in → 1 out7.3700 XPM110 B

AVdK4q4B…qKzkY1qs

c460b48d54cb16…ebdb261588eec0

14 in → 2 out646.7604 XPM2.10 KB

AahkYhUQ…Vka3x4tJ ASceQmR9…YWv9ap8U

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.

5.332 × 10⁹⁵(96-digit number)

53323388854051139293…24411126650568551679

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

5.332 × 10⁹⁵(96-digit number)

53323388854051139293…24411126650568551679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.332 × 10⁹⁵(96-digit number)

53323388854051139293…24411126650568551681

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

1.066 × 10⁹⁶(97-digit number)

10664677770810227858…48822253301137103359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.066 × 10⁹⁶(97-digit number)

10664677770810227858…48822253301137103361

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

2.132 × 10⁹⁶(97-digit number)

21329355541620455717…97644506602274206719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.132 × 10⁹⁶(97-digit number)

21329355541620455717…97644506602274206721

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

4.265 × 10⁹⁶(97-digit number)

42658711083240911434…95289013204548413439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.265 × 10⁹⁶(97-digit number)

42658711083240911434…95289013204548413441

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

8.531 × 10⁹⁶(97-digit number)

85317422166481822869…90578026409096826879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.531 × 10⁹⁶(97-digit number)

85317422166481822869…90578026409096826881

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

1.706 × 10⁹⁷(98-digit number)

17063484433296364573…81156052818193653759

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 #2,872,302

Cookie Preferences