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Block #1,361,021

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/8/2015, 3:31:29 PM Β· Difficulty 10.8411 Β· 5,438,148 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bc22bd9931432463a093d3bcfda3895455ea3d194b52d8d7c595090fe2e9be10
View on Chainz β†—

Height

#1,361,021

Difficulty

10.841114

Transactions

2

Size

13.12 KB

Version

2

Bits

0ad75339

Nonce

85,067,292

Timestamp

12/8/2015, 3:31:29 PM

Confirmations

5,438,148

Mined by

⛏️ P2SHAYcMdpMYA7VzJm9LvQ2jYz3NSZipZn4dRG

Merkle Root

003d605c9aa24766bf4ed64c69e6e5a63152f572cf2e463d0be3fc6a77ae5341
Transactions (2)
Coinbase5cd37f68fc80c2…a956292c202d31
1 in β†’ 1 out8.6500 XPM110 B
AYcMdpMY…ipZn4dRG
95fcf461bb0f63…7fc89a02917b4f
89 in β†’ 2 out494.8570 XPM12.93 KB
AJVeRHXf…C2yREH1fAa7zG9vX…Xk6HEDRC
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.

8.672 Γ— 10⁹²(93-digit number)
86729786513409349425…73660626128525459999
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
8.672 Γ— 10⁹²(93-digit number)
86729786513409349425…73660626128525459999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.734 Γ— 10⁹³(94-digit number)
17345957302681869885…47321252257050919999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.469 Γ— 10⁹³(94-digit number)
34691914605363739770…94642504514101839999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.938 Γ— 10⁹³(94-digit number)
69383829210727479540…89285009028203679999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.387 Γ— 10⁹⁴(95-digit number)
13876765842145495908…78570018056407359999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.775 Γ— 10⁹⁴(95-digit number)
27753531684290991816…57140036112814719999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.550 Γ— 10⁹⁴(95-digit number)
55507063368581983632…14280072225629439999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.110 Γ— 10⁹⁡(96-digit number)
11101412673716396726…28560144451258879999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.220 Γ— 10⁹⁡(96-digit number)
22202825347432793452…57120288902517759999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.440 Γ— 10⁹⁡(96-digit number)
44405650694865586905…14240577805035519999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.881 Γ— 10⁹⁡(96-digit number)
88811301389731173811…28481155610071039999
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:57,637,387 XPMΒ·at block #6,799,168 Β· updates every 60s
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