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Block #1,341,520

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/25/2015, 7:45:16 PM Β· Difficulty 10.8040 Β· 5,469,430 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
44fa523d6bdb70d367264eea4fa39643a6b3ed83fe9b96f098ed0eb927400040
View on Chainz β†—

Height

#1,341,520

Difficulty

10.803976

Transactions

2

Size

50.13 KB

Version

2

Bits

0acdd166

Nonce

141,296,237

Timestamp

11/25/2015, 7:45:16 PM

Confirmations

5,469,430

Mined by

⛏️ P2SHAJ6WYJphai2JxwSpJRduonhKa15KRKf742

Merkle Root

d43f31a114575c15a8e85fdf65e032f8eee2a0e9950d01bed6f67b44685add7a
Transactions (2)
Coinbasebb71de8765f82d…e23f65678640a4
1 in β†’ 1 out9.4400 XPM109 B
AJ6WYJph…5KRKf742
373fd90d6d38b7…904e844664d0ac
345 in β†’ 2 out1542.2500 XPM49.93 KB
AYsTc4jJ…M9Cx3QrvAa6e6Sys…wXYUy8ks
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.

8.874 Γ— 10⁹²(93-digit number)
88745915056008268248…95863766287296561599
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
8.874 Γ— 10⁹²(93-digit number)
88745915056008268248…95863766287296561599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.774 Γ— 10⁹³(94-digit number)
17749183011201653649…91727532574593123199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.549 Γ— 10⁹³(94-digit number)
35498366022403307299…83455065149186246399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.099 Γ— 10⁹³(94-digit number)
70996732044806614598…66910130298372492799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.419 Γ— 10⁹⁴(95-digit number)
14199346408961322919…33820260596744985599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.839 Γ— 10⁹⁴(95-digit number)
28398692817922645839…67640521193489971199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.679 Γ— 10⁹⁴(95-digit number)
56797385635845291678…35281042386979942399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.135 Γ— 10⁹⁡(96-digit number)
11359477127169058335…70562084773959884799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.271 Γ— 10⁹⁡(96-digit number)
22718954254338116671…41124169547919769599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.543 Γ— 10⁹⁡(96-digit number)
45437908508676233342…82248339095839539199
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:57,731,699 XPMΒ·at block #6,810,949 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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