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Block #386,825

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/2/2014, 5:21:40 PM Β· Difficulty 10.4122 Β· 6,411,602 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7e6378ee56ea76c185bc9b6429ecf7d48fb69974dabd28e43a1e6a11b83008c1
View on Chainz β†—

Height

#386,825

Difficulty

10.412180

Transactions

2

Size

505 B

Version

2

Bits

0a698499

Nonce

86,260

Timestamp

2/2/2014, 5:21:40 PM

Confirmations

6,411,602

Mined by

⛏️ P2SHAKdQsc6EDkYDfEDytkoYKorJueqX9cfpZg

Merkle Root

0f9fcc876d253f7de42a5799b94a4223298087039c9b4abbb3c30bf33d87a291
Transactions (2)
Coinbase85b3d0421e4e96…df677ca4da52e1
1 in β†’ 1 out9.2200 XPM109 B
AKdQsc6E…qX9cfpZg
90497eca1455ec…af0aff86434605
2 in β†’ 1 out9.2800 XPM306 B
AaLBYWdH…e9nxsSZs
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.

7.333 Γ— 10⁹³(94-digit number)
73337580470689229253…00479309704356745761
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
7.333 Γ— 10⁹³(94-digit number)
73337580470689229253…00479309704356745761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.466 Γ— 10⁹⁴(95-digit number)
14667516094137845850…00958619408713491521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.933 Γ— 10⁹⁴(95-digit number)
29335032188275691701…01917238817426983041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.867 Γ— 10⁹⁴(95-digit number)
58670064376551383402…03834477634853966081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.173 Γ— 10⁹⁡(96-digit number)
11734012875310276680…07668955269707932161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.346 Γ— 10⁹⁡(96-digit number)
23468025750620553361…15337910539415864321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.693 Γ— 10⁹⁡(96-digit number)
46936051501241106722…30675821078831728641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.387 Γ— 10⁹⁡(96-digit number)
93872103002482213444…61351642157663457281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.877 Γ— 10⁹⁢(97-digit number)
18774420600496442688…22703284315326914561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.754 Γ— 10⁹⁢(97-digit number)
37548841200992885377…45406568630653829121
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:57,631,428 XPMΒ·at block #6,798,426 Β· updates every 60s
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