Block #61,045

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 11:17:50 AM · Difficulty 8.9716 · 6,735,241 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9c4060627bd43cb1c473e0491cca49355d80641d30b401957cb611447ee4e8f3

View on Chainz ↗

Height

#61,045

Difficulty

8.971620

Transactions

Size

199 B

Version

Bits

08f8bc1c

Nonce

181

Timestamp

7/18/2013, 11:17:50 AM

Confirmations

6,735,241

Mined by

⛏️ P2SHAQEbmWMhm3AfNhyeGW1Fbr2Y8UbVPpCt5X

Merkle Root

dbf9d33096d0a94c7f8edee6aabc790c5fb984043b2f730dae43b13861b22ed5

Transactions (1)

Coinbasedbf9d33096d0a9…43b13861b22ed5

1 in → 1 out12.4100 XPM110 B

AQEbmWMh…bVPpCt5X

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.

6.071 × 10⁹¹(92-digit number)

60717915567812845832…93374510393388810639

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

6.071 × 10⁹¹(92-digit number)

60717915567812845832…93374510393388810639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.071 × 10⁹¹(92-digit number)

60717915567812845832…93374510393388810641

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

1.214 × 10⁹²(93-digit number)

12143583113562569166…86749020786777621279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.214 × 10⁹²(93-digit number)

12143583113562569166…86749020786777621281

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

2.428 × 10⁹²(93-digit number)

24287166227125138333…73498041573555242559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.428 × 10⁹²(93-digit number)

24287166227125138333…73498041573555242561

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

4.857 × 10⁹²(93-digit number)

48574332454250276666…46996083147110485119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.857 × 10⁹²(93-digit number)

48574332454250276666…46996083147110485121

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

9.714 × 10⁹²(93-digit number)

97148664908500553332…93992166294220970239

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