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Block #486,448

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/11/2014, 2:32:44 PM Β· Difficulty 10.6264 Β· 6,324,543 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
54d4da80ed49f637fc1bfa3d143b6ebe6f3cb07b7e88b4dfa2c911eddfd95fb4
View on Chainz β†—

Height

#486,448

Difficulty

10.626429

Transactions

2

Size

572 B

Version

2

Bits

0aa05da8

Nonce

153,355,934

Timestamp

4/11/2014, 2:32:44 PM

Confirmations

6,324,543

Mined by

⛏️ P2SHAS17v93WDW5G38fSUVifABzZuPMC6q77tR

Merkle Root

640d0ab597eeb81789994a6dc3fc6ca78ce907e847114f245f7cf3e9c2654cbe
Transactions (2)
Coinbase6d0ae748453844…a7b0296ef8918e
1 in β†’ 1 out8.8500 XPM109 B
AS17v93W…MC6q77tR
0e35704827123a…8d118e01d3bd5b
2 in β†’ 2 out5.0106 XPM374 B
ASMYtQ8s…Y4eiN42eAbZZhdbq…31tzA3Sc
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.

2.542 Γ— 10⁹³(94-digit number)
25423239040561504552…60123144258864667371
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
2.542 Γ— 10⁹³(94-digit number)
25423239040561504552…60123144258864667371
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.084 Γ— 10⁹³(94-digit number)
50846478081123009105…20246288517729334741
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.016 Γ— 10⁹⁴(95-digit number)
10169295616224601821…40492577035458669481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.033 Γ— 10⁹⁴(95-digit number)
20338591232449203642…80985154070917338961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.067 Γ— 10⁹⁴(95-digit number)
40677182464898407284…61970308141834677921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.135 Γ— 10⁹⁴(95-digit number)
81354364929796814568…23940616283669355841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.627 Γ— 10⁹⁡(96-digit number)
16270872985959362913…47881232567338711681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.254 Γ— 10⁹⁡(96-digit number)
32541745971918725827…95762465134677423361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.508 Γ— 10⁹⁡(96-digit number)
65083491943837451654…91524930269354846721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.301 Γ— 10⁹⁢(97-digit number)
13016698388767490330…83049860538709693441
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:57,732,032 XPMΒ·at block #6,810,990 Β· updates every 60s
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