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Block #364,826

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/18/2014, 8:09:13 AM Β· Difficulty 10.4231 Β· 6,465,823 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3a338e705d497305fe9e04b1ebfa3a6dd009c423246ea9ec7cffb40aea6c1b2b
View on Chainz β†—

Height

#364,826

Difficulty

10.423069

Transactions

1

Size

205 B

Version

2

Bits

0a6c4e3b

Nonce

71,861

Timestamp

1/18/2014, 8:09:13 AM

Confirmations

6,465,823

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

ba57953955d1418fdd913a057acc95f1de9896eed1ff9175c3dfad20ae7fec22
Transactions (1)
Coinbaseba57953955d141…dfad20ae7fec22
1 in β†’ 1 out9.1900 XPM116 B
AbwWkWZt…kawDhufa
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.

9.418 Γ— 10⁹²(93-digit number)
94186004245737943566…96861131297091078401
Discovered Prime Numbers
p_k = 2^k Γ— 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.

1
origin + 1
9.418 Γ— 10⁹²(93-digit number)
94186004245737943566…96861131297091078401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.883 Γ— 10⁹³(94-digit number)
18837200849147588713…93722262594182156801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.767 Γ— 10⁹³(94-digit number)
37674401698295177426…87444525188364313601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.534 Γ— 10⁹³(94-digit number)
75348803396590354852…74889050376728627201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.506 Γ— 10⁹⁴(95-digit number)
15069760679318070970…49778100753457254401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.013 Γ— 10⁹⁴(95-digit number)
30139521358636141941…99556201506914508801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.027 Γ— 10⁹⁴(95-digit number)
60279042717272283882…99112403013829017601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.205 Γ— 10⁹⁡(96-digit number)
12055808543454456776…98224806027658035201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.411 Γ— 10⁹⁡(96-digit number)
24111617086908913552…96449612055316070401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.822 Γ— 10⁹⁡(96-digit number)
48223234173817827105…92899224110632140801
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,889,317 XPMΒ·at block #6,830,648 Β· updates every 60s
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