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Block #1,365,136

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/11/2015, 9:37:59 AM Β· Difficulty 10.8459 Β· 5,461,659 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7e8cbdab2c70e3860091945beb5a230a0fd88936b554274741dc38e0ce8efc03
View on Chainz β†—

Height

#1,365,136

Difficulty

10.845893

Transactions

2

Size

425 B

Version

2

Bits

0ad88c75

Nonce

916,884,983

Timestamp

12/11/2015, 9:37:59 AM

Confirmations

5,461,659

Mined by

⛏️ P2SHAH2KY2D8MYHfyXy8UmXVP39RM8tpwUEFGL

Merkle Root

b98ac9aee9b36f59e6f7bf49705fee204c683cd8e016479d494e0af8c326e411
Transactions (2)
Coinbase5e34c3344d65e4…c46aa8b6fff652
1 in β†’ 1 out8.5000 XPM109 B
AH2KY2D8…tpwUEFGL
db32e5fa3a590c…b546fe852502d1
1 in β†’ 2 out5.6508 XPM227 B
ActNif4V…GfJ4Z1RTAKsebF9o…26T4a6vn
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.

1.773 Γ— 10⁹³(94-digit number)
17732616046955376018…73071272504512234241
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
1.773 Γ— 10⁹³(94-digit number)
17732616046955376018…73071272504512234241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.546 Γ— 10⁹³(94-digit number)
35465232093910752037…46142545009024468481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
7.093 Γ— 10⁹³(94-digit number)
70930464187821504074…92285090018048936961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.418 Γ— 10⁹⁴(95-digit number)
14186092837564300814…84570180036097873921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.837 Γ— 10⁹⁴(95-digit number)
28372185675128601629…69140360072195747841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.674 Γ— 10⁹⁴(95-digit number)
56744371350257203259…38280720144391495681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.134 Γ— 10⁹⁡(96-digit number)
11348874270051440651…76561440288782991361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.269 Γ— 10⁹⁡(96-digit number)
22697748540102881303…53122880577565982721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.539 Γ— 10⁹⁡(96-digit number)
45395497080205762607…06245761155131965441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
9.079 Γ— 10⁹⁡(96-digit number)
90790994160411525215…12491522310263930881
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:57,858,522 XPMΒ·at block #6,826,794 Β· updates every 60s
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