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Block #175,209

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/22/2013, 3:36:52 AM Β· Difficulty 9.8635 Β· 6,651,500 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6691a09915ef3fbe68b5eb9d448d8d897d95bd95d5aac62dbc8b5d4915535a29
View on Chainz β†—

Height

#175,209

Difficulty

9.863545

Transactions

1

Size

198 B

Version

2

Bits

09dd1148

Nonce

192,675

Timestamp

9/22/2013, 3:36:52 AM

Confirmations

6,651,500

Mined by

⛏️ P2SHAe6PYBDNs6MFPfqSfG8TyUUBAHjSQhB18y

Merkle Root

ae9efa728f6f1b66be20b821a7ed44e6656c3d5f84dfa78ff67929657c52f09e
Transactions (1)
Coinbaseae9efa728f6f1b…7929657c52f09e
1 in β†’ 1 out10.2600 XPM109 B
Ae6PYBDN…jSQhB18y
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.282 Γ— 10⁹²(93-digit number)
32822274824723026454…42781097939307846919
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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.

1
origin βˆ’ 1
3.282 Γ— 10⁹²(93-digit number)
32822274824723026454…42781097939307846919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.564 Γ— 10⁹²(93-digit number)
65644549649446052908…85562195878615693839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.312 Γ— 10⁹³(94-digit number)
13128909929889210581…71124391757231387679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.625 Γ— 10⁹³(94-digit number)
26257819859778421163…42248783514462775359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.251 Γ— 10⁹³(94-digit number)
52515639719556842326…84497567028925550719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.050 Γ— 10⁹⁴(95-digit number)
10503127943911368465…68995134057851101439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.100 Γ— 10⁹⁴(95-digit number)
21006255887822736930…37990268115702202879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.201 Γ— 10⁹⁴(95-digit number)
42012511775645473861…75980536231404405759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.402 Γ— 10⁹⁴(95-digit number)
84025023551290947722…51961072462808811519
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜†β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
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