Block #61,460

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/18/2013, 1:32:03 PM · Difficulty 8.9732 · 6,728,478 confirmations

1CC

Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header

Block Hash

56ba8e56884882a01e564ec97112430fb7e242871e144fbe13e28490376c6bd2

View on Chainz ↗

Height

#61,460

Difficulty

8.973176

Transactions

Size

1.08 KB

Version

Bits

08f92208

Nonce

149

Timestamp

7/18/2013, 1:32:03 PM

Confirmations

6,728,478

Merkle Root

14dcb8bcd887bc9505e3e69804cb1b87c3492e1bd7b7379f8d060243dcd1c918

Transactions (3)

Coinbase2d8d1ba66b909f…584dff7642ef2c

1 in → 1 out12.4200 XPM110 B

AK1JUKWL…oPR4rN5o

ae6af0315e2c4e…dbe534a31b1bcd

4 in → 1 out900.0000 XPM635 B

AMSC7hJX…qMSkHHU9

393c18b622f769…c3c97e88105f73

2 in → 1 out24.9300 XPM272 B

AMsHHVZu…WaZMT4WA

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.

3.518 × 10⁹¹(92-digit number)

35184798229211326374…90013985719572983519

Discovered Prime Numbers

p_k = 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.

origin − 1

3.518 × 10⁹¹(92-digit number)

35184798229211326374…90013985719572983519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.036 × 10⁹¹(92-digit number)

70369596458422652749…80027971439145967039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.407 × 10⁹²(93-digit number)

14073919291684530549…60055942878291934079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.814 × 10⁹²(93-digit number)

28147838583369061099…20111885756583868159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.629 × 10⁹²(93-digit number)

56295677166738122199…40223771513167736319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.125 × 10⁹³(94-digit number)

11259135433347624439…80447543026335472639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.251 × 10⁹³(94-digit number)

22518270866695248879…60895086052670945279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.503 × 10⁹³(94-digit number)

45036541733390497759…21790172105341890559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.007 × 10⁹³(94-digit number)

90073083466780995519…43580344210683781119

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 Cunningham Chain of the First Kind. 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer