Block #268,028

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/21/2013, 6:39:47 PM · Difficulty 9.9581 · 6,524,110 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

02f5e4cb36498a8f8f37658155bfe96cad638ff6855ac7b2a3438355cbfa2499

View on Chainz ↗

Height

#268,028

Difficulty

9.958121

Transactions

Size

905 B

Version

Bits

09f5476d

Nonce

64,686

Timestamp

11/21/2013, 6:39:47 PM

Confirmations

6,524,110

Merkle Root

8507e4f6934bbcc07ad477f919f9a2e30eed2f751591b35e144121f1b1f5f312

Transactions (2)

Coinbaseb89904e70e8ab4…15c51e1bee2e70

1 in → 2 out10.0800 XPM141 B

AdGRRh1e…QmctLb24 AHsw4d6U…EnM8UXNZ

4a992d40170d2b…68c6aada594ed4

4 in → 2 out283.2315 XPM671 B

AZfJb8KQ…MLda8r4z AVAJNRKB…Kgqdcj4g

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.

1.149 × 10¹⁰²(103-digit number)

11497183563996557601…43970804265422269599

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

1.149 × 10¹⁰²(103-digit number)

11497183563996557601…43970804265422269599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.149 × 10¹⁰²(103-digit number)

11497183563996557601…43970804265422269601

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

2.299 × 10¹⁰²(103-digit number)

22994367127993115203…87941608530844539199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.299 × 10¹⁰²(103-digit number)

22994367127993115203…87941608530844539201

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

4.598 × 10¹⁰²(103-digit number)

45988734255986230406…75883217061689078399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.598 × 10¹⁰²(103-digit number)

45988734255986230406…75883217061689078401

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

9.197 × 10¹⁰²(103-digit number)

91977468511972460813…51766434123378156799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.197 × 10¹⁰²(103-digit number)

91977468511972460813…51766434123378156801

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

1.839 × 10¹⁰³(104-digit number)

18395493702394492162…03532868246756313599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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