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Block #363,422

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/17/2014, 9:54:32 AM Β· Difficulty 10.4140 Β· 6,463,714 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c25fdf8d167ab9744ea22fc1b9463ff580989b32166b738a6b0e758f30e8456e
View on Chainz β†—

Height

#363,422

Difficulty

10.413988

Transactions

1

Size

199 B

Version

2

Bits

0a69fb25

Nonce

225,085

Timestamp

1/17/2014, 9:54:32 AM

Confirmations

6,463,714

Mined by

⛏️ P2SHAJhr6wenio3Wgde7Dyqy4HhXVhDAq9Tpnu

Merkle Root

ee5a53652d5e037a860d064f178e504929a27c52cb520090c49060cbc56c3102
Transactions (1)
Coinbaseee5a53652d5e03…9060cbc56c3102
1 in β†’ 1 out9.2100 XPM109 B
AJhr6wen…DAq9Tpnu
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.

9.651 Γ— 10⁹³(94-digit number)
96512771746235899819…65867965270237777799
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
9.651 Γ— 10⁹³(94-digit number)
96512771746235899819…65867965270237777799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.930 Γ— 10⁹⁴(95-digit number)
19302554349247179963…31735930540475555599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.860 Γ— 10⁹⁴(95-digit number)
38605108698494359927…63471861080951111199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.721 Γ— 10⁹⁴(95-digit number)
77210217396988719855…26943722161902222399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.544 Γ— 10⁹⁡(96-digit number)
15442043479397743971…53887444323804444799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.088 Γ— 10⁹⁡(96-digit number)
30884086958795487942…07774888647608889599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.176 Γ— 10⁹⁡(96-digit number)
61768173917590975884…15549777295217779199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.235 Γ— 10⁹⁢(97-digit number)
12353634783518195176…31099554590435558399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.470 Γ— 10⁹⁢(97-digit number)
24707269567036390353…62199109180871116799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.941 Γ— 10⁹⁢(97-digit number)
49414539134072780707…24398218361742233599
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:57,861,269 XPMΒ·at block #6,827,135 Β· updates every 60s
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