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Block #668,717

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/8/2014, 10:18:34 AM Β· Difficulty 10.9638 Β· 6,133,501 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ecf587e115e58ce0aadb99cb3255731510f3d523b383c5ee4fce688965036631
View on Chainz β†—

Height

#668,717

Difficulty

10.963804

Transactions

3

Size

1.08 KB

Version

2

Bits

0af6bbe1

Nonce

1,010,629,755

Timestamp

8/8/2014, 10:18:34 AM

Confirmations

6,133,501

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f1c4f854524343193a80f863d37218c3fba6a0cd0845d2c7224dc4c927f71911
Transactions (3)
Coinbase0dd16bd4ad0211…c7803be237023c
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
d8c7e2a7e7b26f…57c31f0dabdd07
4 in β†’ 2 out10.0236 XPM667 B
AdouUT3o…oqYnLrrAANkM1CKq…EynX1eYi
7210693bb4b3f1…3541b309752f5f
1 in β†’ 2 out6.1739 XPM227 B
ASEkR768…35s3LmSuAJXuB412…gLG7CXXW
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.

2.268 Γ— 10⁹⁢(97-digit number)
22685741869897029111…01268522749128861119
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
2.268 Γ— 10⁹⁢(97-digit number)
22685741869897029111…01268522749128861119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.537 Γ— 10⁹⁢(97-digit number)
45371483739794058223…02537045498257722239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.074 Γ— 10⁹⁢(97-digit number)
90742967479588116447…05074090996515444479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.814 Γ— 10⁹⁷(98-digit number)
18148593495917623289…10148181993030888959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.629 Γ— 10⁹⁷(98-digit number)
36297186991835246579…20296363986061777919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.259 Γ— 10⁹⁷(98-digit number)
72594373983670493158…40592727972123555839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.451 Γ— 10⁹⁸(99-digit number)
14518874796734098631…81185455944247111679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.903 Γ— 10⁹⁸(99-digit number)
29037749593468197263…62370911888494223359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.807 Γ— 10⁹⁸(99-digit number)
58075499186936394526…24741823776988446719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.161 Γ— 10⁹⁹(100-digit number)
11615099837387278905…49483647553976893439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.323 Γ— 10⁹⁹(100-digit number)
23230199674774557810…98967295107953786879
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,661,750 XPMΒ·at block #6,802,217 Β· updates every 60s
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