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Block #222,365

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/22/2013, 4:21:05 AM Β· Difficulty 9.9397 Β· 6,594,122 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b2c5e2235c9db75d936f297b64f9576ac38b497189805cbfab5f26bd96992810
View on Chainz β†—

Height

#222,365

Difficulty

9.939735

Transactions

1

Size

198 B

Version

2

Bits

09f09274

Nonce

171,751

Timestamp

10/22/2013, 4:21:05 AM

Confirmations

6,594,122

Mined by

⛏️ P2SHAMjEL5jU5FrR33MFDHGMbVsnwkXWAbZRhp

Merkle Root

6df79b4c0f5a487244e49defc9899c7f36471f2f9b33a26aeac49577faa289e6
Transactions (1)
Coinbase6df79b4c0f5a48…c49577faa289e6
1 in β†’ 1 out10.1100 XPM109 B
AMjEL5jU…XWAbZRhp
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.

1.031 Γ— 10⁹³(94-digit number)
10311918921890591585…81313817465665186119
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
1.031 Γ— 10⁹³(94-digit number)
10311918921890591585…81313817465665186119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.062 Γ— 10⁹³(94-digit number)
20623837843781183171…62627634931330372239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.124 Γ— 10⁹³(94-digit number)
41247675687562366343…25255269862660744479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.249 Γ— 10⁹³(94-digit number)
82495351375124732687…50510539725321488959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.649 Γ— 10⁹⁴(95-digit number)
16499070275024946537…01021079450642977919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.299 Γ— 10⁹⁴(95-digit number)
32998140550049893075…02042158901285955839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.599 Γ— 10⁹⁴(95-digit number)
65996281100099786150…04084317802571911679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.319 Γ— 10⁹⁡(96-digit number)
13199256220019957230…08168635605143823359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.639 Γ— 10⁹⁡(96-digit number)
26398512440039914460…16337271210287646719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.279 Γ— 10⁹⁡(96-digit number)
52797024880079828920…32674542420575293439
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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
Circulating Supply:57,776,023 XPMΒ·at block #6,816,486 Β· updates every 60s
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