Block #2,595,454

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/1/2018, 1:50:36 PM · Difficulty 11.2967 · 4,238,196 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ccd9c940e9080cbcaa3af8503c91126556c4db6e9832eb36f48a158b43e76220

View on Chainz ↗

Height

#2,595,454

Difficulty

11.296711

Transactions

Size

726 B

Version

Bits

0b4bf53f

Nonce

403,438,008

Timestamp

4/1/2018, 1:50:36 PM

Confirmations

4,238,196

Mined by

⛏️ P2SHATHitMPHpbjKhrvoyp9qtQTGxtBXFgcYac

Merkle Root

a1cd3ea2e012a2d991ff2a9c1e69ff4ce80311a215f6523b760d5bf6db0d63a2

Transactions (2)

Coinbase104a85af4e93ca…f2607679695423

1 in → 1 out7.8300 XPM110 B

ATHitMPH…BXFgcYac

0562ee938c33da…7705be7fe9259e

3 in → 2 out727.4445 XPM524 B

AHYhsSAy…MEtBM8K1 ANXeG6di…vWWJGaw8

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.

6.845 × 10⁹⁹(100-digit number)

68455001038592136551…21328131801811517439

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

6.845 × 10⁹⁹(100-digit number)

68455001038592136551…21328131801811517439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.845 × 10⁹⁹(100-digit number)

68455001038592136551…21328131801811517441

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

1.369 × 10¹⁰⁰(101-digit number)

13691000207718427310…42656263603623034879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.369 × 10¹⁰⁰(101-digit number)

13691000207718427310…42656263603623034881

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

2.738 × 10¹⁰⁰(101-digit number)

27382000415436854620…85312527207246069759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.738 × 10¹⁰⁰(101-digit number)

27382000415436854620…85312527207246069761

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

5.476 × 10¹⁰⁰(101-digit number)

54764000830873709241…70625054414492139519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.476 × 10¹⁰⁰(101-digit number)

54764000830873709241…70625054414492139521

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

1.095 × 10¹⁰¹(102-digit number)

10952800166174741848…41250108828984279039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.095 × 10¹⁰¹(102-digit number)

10952800166174741848…41250108828984279041

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

2.190 × 10¹⁰¹(102-digit number)

21905600332349483696…82500217657968558079

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 #2,595,454

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