Block #71,836

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 8:44:34 PM · Difficulty 8.9936 · 6,719,582 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e5fce56158a5d243eda70e5df88cd83e9cac3f10deb9b751aa64484a9a7ab33b

View on Chainz ↗

Height

#71,836

Difficulty

8.993563

Transactions

Size

199 B

Version

Bits

08fe5a1d

Nonce

245

Timestamp

7/20/2013, 8:44:34 PM

Confirmations

6,719,582

Merkle Root

46765522b7697a0d3fa21bcd0c10c17cb53de3321332290cdf400fcda321736d

Transactions (1)

Coinbase46765522b7697a…400fcda321736d

1 in → 1 out12.3500 XPM110 B

ANCYL9xh…9WyGnqDE

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.

1.973 × 10⁹²(93-digit number)

19730765662993250660…32703781878519520519

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

1.973 × 10⁹²(93-digit number)

19730765662993250660…32703781878519520519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.973 × 10⁹²(93-digit number)

19730765662993250660…32703781878519520521

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

3.946 × 10⁹²(93-digit number)

39461531325986501320…65407563757039041039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.946 × 10⁹²(93-digit number)

39461531325986501320…65407563757039041041

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

7.892 × 10⁹²(93-digit number)

78923062651973002641…30815127514078082079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.892 × 10⁹²(93-digit number)

78923062651973002641…30815127514078082081

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

1.578 × 10⁹³(94-digit number)

15784612530394600528…61630255028156164159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.578 × 10⁹³(94-digit number)

15784612530394600528…61630255028156164161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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