Block #64,824

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 9:19:54 AM · Difficulty 8.9827 · 6,728,289 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

67cd14bfadcc799717226004f26d305eb5c9c5ff6b94dee4a9f44dcb030cf66f

View on Chainz ↗

Height

#64,824

Difficulty

8.982667

Transactions

Size

204 B

Version

Bits

08fb9009

Nonce

Timestamp

7/19/2013, 9:19:54 AM

Confirmations

6,728,289

Merkle Root

4ce67e3da7727a0f6532d2b0933a0aea95c96b89f0576178b190fbe5327d8403

Transactions (1)

Coinbase4ce67e3da7727a…90fbe5327d8403

1 in → 1 out12.3800 XPM110 B

AGY4TBx7…YfD8h7Va

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.

1.979 × 10¹⁰³(104-digit number)

19793945824923911937…79232861278392416619

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

1.979 × 10¹⁰³(104-digit number)

19793945824923911937…79232861278392416619

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.979 × 10¹⁰³(104-digit number)

19793945824923911937…79232861278392416621

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

3.958 × 10¹⁰³(104-digit number)

39587891649847823875…58465722556784833239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.958 × 10¹⁰³(104-digit number)

39587891649847823875…58465722556784833241

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

7.917 × 10¹⁰³(104-digit number)

79175783299695647750…16931445113569666479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.917 × 10¹⁰³(104-digit number)

79175783299695647750…16931445113569666481

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

1.583 × 10¹⁰⁴(105-digit number)

15835156659939129550…33862890227139332959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.583 × 10¹⁰⁴(105-digit number)

15835156659939129550…33862890227139332961

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

3.167 × 10¹⁰⁴(105-digit number)

31670313319878259100…67725780454278665919

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