Block #2,559,894

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/11/2018, 6:47:16 AM · Difficulty 10.9919 · 4,283,093 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

231673b9ad347623436709f260dd1986e91aff26ad214e22240a628bcaf52a0a

View on Chainz ↗

Height

#2,559,894

Difficulty

10.991937

Transactions

Size

1021 B

Version

Bits

0afdef93

Nonce

431,043,316

Timestamp

3/11/2018, 6:47:16 AM

Confirmations

4,283,093

Mined by

⛏️ P2SHAQjifaDX11CKvHfR4UqvJwHRNn2NR6capZ

Merkle Root

ec4df0203b2f27bdb66ae9d3ca13507a21c961bd64c93287d29d1ec6f9ce334d

Transactions (2)

Coinbase643d6003594223…e7a9cb1d52ce15

1 in → 1 out8.2700 XPM110 B

AQjifaDX…2NR6capZ

760b5fa2702634…5bfdbfcfd7a2d7

5 in → 2 out16.6400 XPM820 B

AXFArXwD…ZjT5Juh6 AU3otget…nux3eV2w

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.

2.643 × 10⁹⁶(97-digit number)

26435773718455131513…03658595443626970879

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

2.643 × 10⁹⁶(97-digit number)

26435773718455131513…03658595443626970879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.643 × 10⁹⁶(97-digit number)

26435773718455131513…03658595443626970881

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

5.287 × 10⁹⁶(97-digit number)

52871547436910263026…07317190887253941759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.287 × 10⁹⁶(97-digit number)

52871547436910263026…07317190887253941761

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

1.057 × 10⁹⁷(98-digit number)

10574309487382052605…14634381774507883519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.057 × 10⁹⁷(98-digit number)

10574309487382052605…14634381774507883521

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

2.114 × 10⁹⁷(98-digit number)

21148618974764105210…29268763549015767039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.114 × 10⁹⁷(98-digit number)

21148618974764105210…29268763549015767041

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

4.229 × 10⁹⁷(98-digit number)

42297237949528210421…58537527098031534079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.229 × 10⁹⁷(98-digit number)

42297237949528210421…58537527098031534081

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

8.459 × 10⁹⁷(98-digit number)

84594475899056420843…17075054196063068159

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 #2,559,894

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