Block #233,167

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/29/2013, 1:28:36 PM · Difficulty 9.9422 · 6,562,425 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

90fedf9d055e5287fe2e81cc9e5d4c97dea0cbe8110afa90100eb54e33eaffab

View on Chainz ↗

Height

#233,167

Difficulty

9.942227

Transactions

Size

1.64 KB

Version

Bits

09f135d0

Nonce

64,294

Timestamp

10/29/2013, 1:28:36 PM

Confirmations

6,562,425

Mined by

⛏️ RoAJaGRnajU4FKPNSjrHvpAByLABiCHGoy6E

Merkle Root

009d167c7f8db746d6b5ecdaac4decb53b04be99892a245b42a5bb3ce71aa75c

Transactions (1)

Coinbase009d167c7f8db7…a5bb3ce71aa75c

1 in → 45 out10.0800 XPM1.55 KB

AJaGRnaj…iCHGoy6E ARpndEmc…Hg792kEk AG9H2B8p…eiaSPdGS AZWiC56x…NwextJca AcEnwywz…vZtt2xTs

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.

3.320 × 10⁹²(93-digit number)

33203179350728794503…07823871483663260959

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

3.320 × 10⁹²(93-digit number)

33203179350728794503…07823871483663260959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.640 × 10⁹²(93-digit number)

66406358701457589006…15647742967326521919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.328 × 10⁹³(94-digit number)

13281271740291517801…31295485934653043839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.656 × 10⁹³(94-digit number)

26562543480583035602…62590971869306087679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.312 × 10⁹³(94-digit number)

53125086961166071205…25181943738612175359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.062 × 10⁹⁴(95-digit number)

10625017392233214241…50363887477224350719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.125 × 10⁹⁴(95-digit number)

21250034784466428482…00727774954448701439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.250 × 10⁹⁴(95-digit number)

42500069568932856964…01455549908897402879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.500 × 10⁹⁴(95-digit number)

85000139137865713928…02911099817794805759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.700 × 10⁹⁵(96-digit number)

17000027827573142785…05822199635589611519

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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