Block #269,041

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/22/2013, 4:44:49 PM · Difficulty 9.9555 · 6,530,304 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8236642b97dc8afdab83ae3d03301da73adcd255dd80672995ec3a510c44829a

View on Chainz ↗

Height

#269,041

Difficulty

9.955491

Transactions

Size

4.62 KB

Version

Bits

09f49b12

Nonce

78,491

Timestamp

11/22/2013, 4:44:49 PM

Confirmations

6,530,304

Mined by

⛏️ aR8AReBFi8Qw3CBboJ1FFYhnJVQZhQq1cm1uS

Merkle Root

fbd25c07d19e83f84418e20f7ade0c61a372707e6dd45d9687f301414ce79d04

Transactions (4)

Coinbase948324fff444ea…593d0c982fe093

1 in → 54 out10.0500 XPM1.85 KB

AReBFi8Q…Qq1cm1uS APZy8y6E…QZaGQjfp ANHbaxZp…XjnHCJJs AVzhvfTX…ZzNJYq61 APeshfYV…3PKcKMKH

745d782bcd4e7b…03b3f70d232401

1 in → 2 out1199.9900 XPM225 B

AJ3M55oz…LbpyS75y AWjmhp34…Qwzar9Sn

ba3fdb38297014…e0be054157157b

11 in → 2 out177.6297 XPM1.66 KB

AMsy2uAu…U5eNE21s AJ3xC1FC…FfwGprVw

b597b9e1cf72af…4d27d9633436d5

5 in → 2 out171.6108 XPM817 B

AMsy2uAu…U5eNE21s AW2EG9Rp…x7zztgEh

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.

3.277 × 10⁹⁴(95-digit number)

32776685116368398532…14479992464473978879

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

3.277 × 10⁹⁴(95-digit number)

32776685116368398532…14479992464473978879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.277 × 10⁹⁴(95-digit number)

32776685116368398532…14479992464473978881

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

6.555 × 10⁹⁴(95-digit number)

65553370232736797064…28959984928947957759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.555 × 10⁹⁴(95-digit number)

65553370232736797064…28959984928947957761

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

1.311 × 10⁹⁵(96-digit number)

13110674046547359412…57919969857895915519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.311 × 10⁹⁵(96-digit number)

13110674046547359412…57919969857895915521

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

2.622 × 10⁹⁵(96-digit number)

26221348093094718825…15839939715791831039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.622 × 10⁹⁵(96-digit number)

26221348093094718825…15839939715791831041

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

5.244 × 10⁹⁵(96-digit number)

52442696186189437651…31679879431583662079

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