Block #78,872

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/23/2013, 4:02:30 AM · Difficulty 9.2297 · 6,712,120 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23f09f2d7177fbd96e58eed675245561fe59e414ee7fb74b64c0de5ebf7a6bf0

View on Chainz ↗

Height

#78,872

Difficulty

9.229726

Transactions

Size

716 B

Version

Bits

093acf52

Nonce

266

Timestamp

7/23/2013, 4:02:30 AM

Confirmations

6,712,120

Merkle Root

db702ca69e68d4eabc8ca7cf9ba11ddaed1a0ea40d472d0cafb67d2ef95899cf

Transactions (4)

Coinbase60fe96aad0043a…348b79aa06fd0f

1 in → 1 out11.7500 XPM110 B

AWZtDe8T…4aCEBT54

a7d59e5a1ac89c…70f39eefc53dfa

1 in → 2 out12.7900 XPM191 B

APwLy6FT…Yzbdv5Mc AG2vUcD1…EjGhzrT9

9404e5e2081f3e…f47a9fc68c7ed9

1 in → 1 out12.3100 XPM159 B

ASj7fWPU…by8b9uAs

4fdcab301b7c64…3e1b4766b3bf9f

1 in → 1 out12.2600 XPM158 B

ASEZYuWi…HLFGddyN

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.

7.941 × 10¹¹⁴(115-digit number)

79418245753231437287…14105356829573368829

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

7.941 × 10¹¹⁴(115-digit number)

79418245753231437287…14105356829573368829

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.941 × 10¹¹⁴(115-digit number)

79418245753231437287…14105356829573368831

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

1.588 × 10¹¹⁵(116-digit number)

15883649150646287457…28210713659146737659

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.588 × 10¹¹⁵(116-digit number)

15883649150646287457…28210713659146737661

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

3.176 × 10¹¹⁵(116-digit number)

31767298301292574915…56421427318293475319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.176 × 10¹¹⁵(116-digit number)

31767298301292574915…56421427318293475321

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

6.353 × 10¹¹⁵(116-digit number)

63534596602585149830…12842854636586950639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.353 × 10¹¹⁵(116-digit number)

63534596602585149830…12842854636586950641

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

1.270 × 10¹¹⁶(117-digit number)

12706919320517029966…25685709273173901279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.270 × 10¹¹⁶(117-digit number)

12706919320517029966…25685709273173901281

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