Block #2,655,299

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/10/2018, 1:48:17 AM · Difficulty 11.7078 · 4,178,598 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

68767d35945867b0f9c6eb5d40cfe5a195d8f864890249f6938bf940860cc148

View on Chainz ↗

Height

#2,655,299

Difficulty

11.707835

Transactions

Size

428 B

Version

Bits

0bb534b5

Nonce

245,346,437

Timestamp

5/10/2018, 1:48:17 AM

Confirmations

4,178,598

Mined by

⛏️ P2SHAJUUnkXoQGbiex6gdyJPo4HYkbR3r9gP3C

Merkle Root

237cdcce268ceeecf7e1d7a225befe747dae8cedf0953197a1136e4a0f75f88f

Transactions (2)

Coinbase0aed4dedbd7bed…ca82e794b54ffe

1 in → 1 out7.2900 XPM110 B

AJUUnkXo…R3r9gP3C

1c1bebc098ebd7…98c20df105ba1f

1 in → 2 out229.7472 XPM227 B

AWnCDvWd…dtaZN8ZS AMiSMLP5…oQNvdfyn

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.

1.060 × 10⁹⁸(99-digit number)

10601806642564629458…02550300505517588479

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

1.060 × 10⁹⁸(99-digit number)

10601806642564629458…02550300505517588479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.060 × 10⁹⁸(99-digit number)

10601806642564629458…02550300505517588481

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

2.120 × 10⁹⁸(99-digit number)

21203613285129258917…05100601011035176959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.120 × 10⁹⁸(99-digit number)

21203613285129258917…05100601011035176961

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

4.240 × 10⁹⁸(99-digit number)

42407226570258517834…10201202022070353919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.240 × 10⁹⁸(99-digit number)

42407226570258517834…10201202022070353921

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

8.481 × 10⁹⁸(99-digit number)

84814453140517035668…20402404044140707839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.481 × 10⁹⁸(99-digit number)

84814453140517035668…20402404044140707841

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

1.696 × 10⁹⁹(100-digit number)

16962890628103407133…40804808088281415679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.696 × 10⁹⁹(100-digit number)

16962890628103407133…40804808088281415681

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

3.392 × 10⁹⁹(100-digit number)

33925781256206814267…81609616176562831359

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 #2,655,299

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