Block #2,701,584

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/12/2018, 1:40:08 AM · Difficulty 11.6291 · 4,129,820 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e0c1af71352d0ce23f79a8a51bc9ee44d28d08243b3a9c7509734d66156be588

View on Chainz ↗

Height

#2,701,584

Difficulty

11.629122

Transactions

Size

869 B

Version

Bits

0ba10e1f

Nonce

2,024,358,417

Timestamp

6/12/2018, 1:40:08 AM

Confirmations

4,129,820

Mined by

⛏️ P2SHAWSTwB8by1o1KdLugM4bze4pGXW4xFkgyf

Merkle Root

40b928123ed03db999987ee82fc4b75b4e71b0cf2fccc8295d19b2f1a5f5fecd

Transactions (2)

Coinbase4931f0684600d8…ebcad7e6ff64c2

1 in → 1 out7.3900 XPM110 B

AWSTwB8b…W4xFkgyf

54a28ecef137b8…fc867a03f6a894

4 in → 2 out600.0101 XPM668 B

AQmjqzoU…5U6sbve9 AbGyA6Ud…tMZhJPKh

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.

2.126 × 10⁹⁶(97-digit number)

21260524740629382014…94519328900191544319

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

2.126 × 10⁹⁶(97-digit number)

21260524740629382014…94519328900191544319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.126 × 10⁹⁶(97-digit number)

21260524740629382014…94519328900191544321

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

4.252 × 10⁹⁶(97-digit number)

42521049481258764028…89038657800383088639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.252 × 10⁹⁶(97-digit number)

42521049481258764028…89038657800383088641

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

8.504 × 10⁹⁶(97-digit number)

85042098962517528056…78077315600766177279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.504 × 10⁹⁶(97-digit number)

85042098962517528056…78077315600766177281

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

1.700 × 10⁹⁷(98-digit number)

17008419792503505611…56154631201532354559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.700 × 10⁹⁷(98-digit number)

17008419792503505611…56154631201532354561

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

3.401 × 10⁹⁷(98-digit number)

34016839585007011222…12309262403064709119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.401 × 10⁹⁷(98-digit number)

34016839585007011222…12309262403064709121

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

6.803 × 10⁹⁷(98-digit number)

68033679170014022445…24618524806129418239

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 #2,701,584

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