Block #76,443

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/22/2013, 12:34:48 AM · Difficulty 9.0988 · 6,714,975 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

febb72b501d522d6e527ac407085fa82c0705424ad89e42b421e5aaa0f14db95

View on Chainz ↗

Height

#76,443

Difficulty

9.098822

Transactions

Size

731 B

Version

Bits

09194c66

Nonce

135

Timestamp

7/22/2013, 12:34:48 AM

Confirmations

6,714,975

Merkle Root

8955c206cbf320d22723f69501aaa39bfd8e4783a05fd929bfe6341eb3b7d189

Transactions (2)

Coinbase11a2c2eeea0c27…35c30934f0ab18

1 in → 1 out12.0700 XPM110 B

ASUmFvxq…6mrDAKEZ

defcec297ffa4e…f82af1291b212c

4 in → 2 out49.3500 XPM531 B

AZiCNyEn…BjhGoBch AYRToess…2AYjYmfp

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.

1.225 × 10⁹⁵(96-digit number)

12259178343288910642…84343854922147814959

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

1.225 × 10⁹⁵(96-digit number)

12259178343288910642…84343854922147814959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.225 × 10⁹⁵(96-digit number)

12259178343288910642…84343854922147814961

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

2.451 × 10⁹⁵(96-digit number)

24518356686577821284…68687709844295629919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.451 × 10⁹⁵(96-digit number)

24518356686577821284…68687709844295629921

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

4.903 × 10⁹⁵(96-digit number)

49036713373155642569…37375419688591259839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.903 × 10⁹⁵(96-digit number)

49036713373155642569…37375419688591259841

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

9.807 × 10⁹⁵(96-digit number)

98073426746311285138…74750839377182519679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.807 × 10⁹⁵(96-digit number)

98073426746311285138…74750839377182519681

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

1.961 × 10⁹⁶(97-digit number)

19614685349262257027…49501678754365039359

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