Block #268,443

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 3:33:47 AM · Difficulty 9.9571 · 6,525,745 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e78c1915bded650c20d66303d1b22823b7e3e902d5f00658ab788122a471dd0

View on Chainz ↗

Height

#268,443

Difficulty

9.957133

Transactions

Size

3.75 KB

Version

Bits

09f506a8

Nonce

18,128

Timestamp

11/22/2013, 3:33:47 AM

Confirmations

6,525,745

Merkle Root

5be4eb30b1170bb391695c2d97eb8312131aa0356581c5a05773e2b58b64bbc8

Transactions (4)

Coinbase5f0f93843018af…582e8259da0464

1 in → 1 out10.1300 XPM109 B

AbfrYgdT…QxENkBYy

056b3b343c954c…88b646ab12fefa

2 in → 2 out99.1918 XPM373 B

AX65w2u1…U9FMmnRi AJUC9rkZ…mPSAsn99

a916e0c1ea36d7…ff0683fc263d73

20 in → 2 out2.7862 XPM2.97 KB

Acf39C89…aMDnU3XF Adkgee8h…KNEAFGxW

b34212ebf49410…0808501c134f6e

1 in → 2 out4.0089 XPM225 B

AWdbTeXM…Z6TaqsCD AFwGUVRK…gZbeEDZ4

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.

1.503 × 10⁹³(94-digit number)

15034628293844759396…63442070198032674879

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

1.503 × 10⁹³(94-digit number)

15034628293844759396…63442070198032674879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.503 × 10⁹³(94-digit number)

15034628293844759396…63442070198032674881

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

3.006 × 10⁹³(94-digit number)

30069256587689518792…26884140396065349759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.006 × 10⁹³(94-digit number)

30069256587689518792…26884140396065349761

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

6.013 × 10⁹³(94-digit number)

60138513175379037584…53768280792130699519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.013 × 10⁹³(94-digit number)

60138513175379037584…53768280792130699521

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

1.202 × 10⁹⁴(95-digit number)

12027702635075807516…07536561584261399039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.202 × 10⁹⁴(95-digit number)

12027702635075807516…07536561584261399041

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

2.405 × 10⁹⁴(95-digit number)

24055405270151615033…15073123168522798079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.405 × 10⁹⁴(95-digit number)

24055405270151615033…15073123168522798081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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