Block #283,409

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/29/2013, 5:36:39 PM · Difficulty 9.9811 · 6,524,932 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d7679aacacd09bd8f7b000580b6f331c20d6ecea88e2991dc460e346afe6dc4f

View on Chainz ↗

Height

#283,409

Difficulty

9.981062

Transactions

Size

1.83 KB

Version

Bits

09fb26dc

Nonce

29,297

Timestamp

11/29/2013, 5:36:39 PM

Confirmations

6,524,932

Mined by

⛏️ SaRAKde1i4dpqpgDtEArAY3oRXX8K88R1bw6g

Merkle Root

f7d356e0a791b44493968d53c1dd621799c1643705769d9b12a211c42e9bdc85

Transactions (2)

Coinbase70af12df1e440e…6024e5763beb2b

1 in → 31 out10.0000 XPM1.09 KB

AKde1i4d…88R1bw6g AVss9H5F…zXhyMijY AGFAJ5YL…ZEnBbk6G Acs9SHrk…QJSB8SFG AQmTPDxR…qwmJq2NW

33ea1bd4405cfc…83cb41defabddd

4 in → 2 out42.8257 XPM670 B

ALLQt5M5…4wkjC51o AWYtJPoE…1W2UzPiE

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.

3.168 × 10⁹⁴(95-digit number)

31685354033889823114…62418320287935249599

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

3.168 × 10⁹⁴(95-digit number)

31685354033889823114…62418320287935249599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.168 × 10⁹⁴(95-digit number)

31685354033889823114…62418320287935249601

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

6.337 × 10⁹⁴(95-digit number)

63370708067779646228…24836640575870499199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.337 × 10⁹⁴(95-digit number)

63370708067779646228…24836640575870499201

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

1.267 × 10⁹⁵(96-digit number)

12674141613555929245…49673281151740998399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.267 × 10⁹⁵(96-digit number)

12674141613555929245…49673281151740998401

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

2.534 × 10⁹⁵(96-digit number)

25348283227111858491…99346562303481996799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.534 × 10⁹⁵(96-digit number)

25348283227111858491…99346562303481996801

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

5.069 × 10⁹⁵(96-digit number)

50696566454223716982…98693124606963993599

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

Block #283,409

Cookie Preferences