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Block #2,041,334

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/27/2017, 11:09:40 PM Β· Difficulty 10.6732 Β· 4,800,763 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4bf8d9517d222bd7d798b98012e12590b3432a9b85bc7c66d9632022b6503a0c
View on Chainz β†—

Height

#2,041,334

Difficulty

10.673181

Transactions

2

Size

1.42 KB

Version

2

Bits

0aac558f

Nonce

705,291,371

Timestamp

3/27/2017, 11:09:40 PM

Confirmations

4,800,763

Mined by

⛏️ P2SHAQMnfcu32vtLNbLDikyWKHsoaksoqhAE6S

Merkle Root

33524d0e8274a381c04c15f31c672297db21bc29166a10a4428cf4e05c94030a
Transactions (2)
Coinbase9268d189b1c76f…6abe5acd313738
1 in β†’ 1 out8.7800 XPM109 B
AQMnfcu3…soqhAE6S
3acf7fed59fa77…167bd9f8bee9b3
8 in β†’ 2 out9.9907 XPM1.23 KB
AQoY7sz1…VkvsMVNJAdU1JddK…s77E16Ku
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.

2.985 Γ— 10⁹⁡(96-digit number)
29856389071918622252…47849476481488753279
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
2.985 Γ— 10⁹⁡(96-digit number)
29856389071918622252…47849476481488753279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.971 Γ— 10⁹⁡(96-digit number)
59712778143837244505…95698952962977506559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.194 Γ— 10⁹⁢(97-digit number)
11942555628767448901…91397905925955013119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.388 Γ— 10⁹⁢(97-digit number)
23885111257534897802…82795811851910026239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.777 Γ— 10⁹⁢(97-digit number)
47770222515069795604…65591623703820052479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.554 Γ— 10⁹⁢(97-digit number)
95540445030139591208…31183247407640104959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.910 Γ— 10⁹⁷(98-digit number)
19108089006027918241…62366494815280209919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.821 Γ— 10⁹⁷(98-digit number)
38216178012055836483…24732989630560419839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.643 Γ— 10⁹⁷(98-digit number)
76432356024111672967…49465979261120839679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.528 Γ— 10⁹⁸(99-digit number)
15286471204822334593…98931958522241679359
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:57,981,162 XPMΒ·at block #6,842,096 Β· updates every 60s
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