Block #91,347

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/31/2013, 9:07:03 PM · Difficulty 9.2198 · 6,698,532 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6f48c4703b5e10873705dd9885a48d0af0722bb315890fc7e23bba5451a47bcb

View on Chainz ↗

Height

#91,347

Difficulty

9.219792

Transactions

Size

1013 B

Version

Bits

09384443

Nonce

145,091

Timestamp

7/31/2013, 9:07:03 PM

Confirmations

6,698,532

Merkle Root

f15e383984b9bc377d675ff161172e28ca388f431e09b7e297371e8bfbc9616a

Transactions (3)

Coinbaseb8da2ec5c6ab96…fe9506c2764d50

1 in → 1 out11.7700 XPM109 B

ATjDSwt2…8g342rwB

16ca043363eba4…8bfc7e3f572159

3 in → 2 out37.7400 XPM420 B

AYxoT5K3…VLfpXK9w AcAb2hRg…t1YaZXD2

96d3b9d4c85d77…4cee9295251591

3 in → 1 out34.7300 XPM385 B

AYDJFTKL…xxgyoYEU

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.

3.030 × 10¹¹⁶(117-digit number)

30301295340300580656…41343100250715926439

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

3.030 × 10¹¹⁶(117-digit number)

30301295340300580656…41343100250715926439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.030 × 10¹¹⁶(117-digit number)

30301295340300580656…41343100250715926441

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

6.060 × 10¹¹⁶(117-digit number)

60602590680601161313…82686200501431852879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.060 × 10¹¹⁶(117-digit number)

60602590680601161313…82686200501431852881

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

1.212 × 10¹¹⁷(118-digit number)

12120518136120232262…65372401002863705759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.212 × 10¹¹⁷(118-digit number)

12120518136120232262…65372401002863705761

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

2.424 × 10¹¹⁷(118-digit number)

24241036272240464525…30744802005727411519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.424 × 10¹¹⁷(118-digit number)

24241036272240464525…30744802005727411521

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

4.848 × 10¹¹⁷(118-digit number)

48482072544480929050…61489604011454823039

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