Block #67,711

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 12:22:23 AM · Difficulty 8.9884 · 6,728,574 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d1ae4f8380f9646345fd1bb3cf846d88672d7387de3b2f29225ec98c02451cc3

View on Chainz ↗

Height

#67,711

Difficulty

8.988383

Transactions

Size

574 B

Version

Bits

08fd06a6

Nonce

688

Timestamp

7/20/2013, 12:22:23 AM

Confirmations

6,728,574

Mined by

⛏️ P2SHAc5SPV5RnyWZMdHmV54LiNtKpzMZpuXE6Z

Merkle Root

5734330c8b1c382668b96d915ad2b5fec0d3b03d3dd2128c6c01278238985d22

Transactions (2)

Coinbaseca1ec89f8f29de…0025436e080385

1 in → 1 out12.3700 XPM110 B

Ac5SPV5R…MZpuXE6Z

d8571181c08178…01698b7ebbca40

2 in → 2 out75.1000 XPM374 B

AP1WsuTc…XzK3G23n ASDLQCso…BFWys2FC

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.

1.529 × 10⁹⁴(95-digit number)

15298701504985081345…66513087249990569249

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

1.529 × 10⁹⁴(95-digit number)

15298701504985081345…66513087249990569249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.529 × 10⁹⁴(95-digit number)

15298701504985081345…66513087249990569251

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

3.059 × 10⁹⁴(95-digit number)

30597403009970162690…33026174499981138499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.059 × 10⁹⁴(95-digit number)

30597403009970162690…33026174499981138501

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

6.119 × 10⁹⁴(95-digit number)

61194806019940325380…66052348999962276999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.119 × 10⁹⁴(95-digit number)

61194806019940325380…66052348999962277001

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

1.223 × 10⁹⁵(96-digit number)

12238961203988065076…32104697999924553999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.223 × 10⁹⁵(96-digit number)

12238961203988065076…32104697999924554001

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

2.447 × 10⁹⁵(96-digit number)

24477922407976130152…64209395999849107999

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