Block #2,647,163

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/3/2018, 7:01:13 PM · Difficulty 11.7559 · 4,189,378 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

59637c7fcce14f3f163b866399a04882d54dd4e1f018a7d780873e271ab17a96

View on Chainz ↗

Height

#2,647,163

Difficulty

11.755890

Transactions

Size

725 B

Version

Bits

0bc1820a

Nonce

862,721,241

Timestamp

5/3/2018, 7:01:13 PM

Confirmations

4,189,378

Mined by

⛏️ P2SHAUDUCBsY2gMN63FDkJLAroB6tbFqpK4suu

Merkle Root

f097d4f5178275d778419ac4bab76f4088de2cfb47b142e17c97b8305bccdee1

Transactions (2)

Coinbased5d4823765b17f…080cf9ed756753

1 in → 1 out7.2300 XPM110 B

AUDUCBsY…FqpK4suu

0901e4cf04a487…c0ce46ee04458a

3 in → 2 out4281.1100 XPM524 B

AexSTnwL…zii1j2QG AW8qhT99…4sSksquE

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.

7.571 × 10⁹⁶(97-digit number)

75710494380289280423…60370941811115089919

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

7.571 × 10⁹⁶(97-digit number)

75710494380289280423…60370941811115089919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.571 × 10⁹⁶(97-digit number)

75710494380289280423…60370941811115089921

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

1.514 × 10⁹⁷(98-digit number)

15142098876057856084…20741883622230179839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.514 × 10⁹⁷(98-digit number)

15142098876057856084…20741883622230179841

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

3.028 × 10⁹⁷(98-digit number)

30284197752115712169…41483767244460359679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.028 × 10⁹⁷(98-digit number)

30284197752115712169…41483767244460359681

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

6.056 × 10⁹⁷(98-digit number)

60568395504231424338…82967534488920719359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.056 × 10⁹⁷(98-digit number)

60568395504231424338…82967534488920719361

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

1.211 × 10⁹⁸(99-digit number)

12113679100846284867…65935068977841438719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.211 × 10⁹⁸(99-digit number)

12113679100846284867…65935068977841438721

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

2.422 × 10⁹⁸(99-digit number)

24227358201692569735…31870137955682877439

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 #2,647,163

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