Block #121,781

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/18/2013, 1:02:36 AM · Difficulty 9.7549 · 6,668,053 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ecbea941e78c6fc378a368e39a4aec4e0a460b21917073149bb9cca17db79e33

View on Chainz ↗

Height

#121,781

Difficulty

9.754889

Transactions

Size

200 B

Version

Bits

09c14063

Nonce

16,243

Timestamp

8/18/2013, 1:02:36 AM

Confirmations

6,668,053

Merkle Root

8a4e63179d02395fa3cadf82f9aab8d9e9940f98639d1e7f2c5ed709593479b3

Transactions (1)

Coinbase8a4e63179d0239…5ed709593479b3

1 in → 1 out10.4900 XPM109 B

AZv7gMUK…CbiASjGW

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.

8.480 × 10⁹⁷(98-digit number)

84803509737854804996…32647590585395927041

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

8.480 × 10⁹⁷(98-digit number)

84803509737854804996…32647590585395927041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.696 × 10⁹⁸(99-digit number)

16960701947570960999…65295181170791854081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.392 × 10⁹⁸(99-digit number)

33921403895141921998…30590362341583708161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.784 × 10⁹⁸(99-digit number)

67842807790283843996…61180724683167416321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.356 × 10⁹⁹(100-digit number)

13568561558056768799…22361449366334832641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.713 × 10⁹⁹(100-digit number)

27137123116113537598…44722898732669665281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.427 × 10⁹⁹(100-digit number)

54274246232227075197…89445797465339330561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.085 × 10¹⁰⁰(101-digit number)

10854849246445415039…78891594930678661121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.170 × 10¹⁰⁰(101-digit number)

21709698492890830078…57783189861357322241

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 Second 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 2CC formula:

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

Cross-reference on Chainz Explorer