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Block #528,731

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/6/2014, 7:46:26 PM Β· Difficulty 10.8881 Β· 6,278,149 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a7aadec9cbae0a51e32841f21922ddcb315f4e8feb4b3f744b74ee3f8621b6f4
View on Chainz β†—

Height

#528,731

Difficulty

10.888084

Transactions

2

Size

2.13 KB

Version

2

Bits

0ae35973

Nonce

19,915,296

Timestamp

5/6/2014, 7:46:26 PM

Confirmations

6,278,149

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

75034881ecacdaa979b51c24ff24de3551943ccf80d61439a9e619bd319d956b
Transactions (2)
Coinbasee01c54ebff181b…fb7e6561920be6
1 in β†’ 1 out8.4500 XPM116 B
ANSXnLY2…Sd25TjkD
877d909e95850b…51f6dec96a9085
13 in β†’ 1 out39.0254 XPM1.92 KB
AYfGXBG3…s4uNnsy3
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.

1.697 Γ— 10⁹⁹(100-digit number)
16973082715742348672…73894816462717845439
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
1.697 Γ— 10⁹⁹(100-digit number)
16973082715742348672…73894816462717845439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.394 Γ— 10⁹⁹(100-digit number)
33946165431484697344…47789632925435690879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.789 Γ— 10⁹⁹(100-digit number)
67892330862969394688…95579265850871381759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.357 Γ— 10¹⁰⁰(101-digit number)
13578466172593878937…91158531701742763519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.715 Γ— 10¹⁰⁰(101-digit number)
27156932345187757875…82317063403485527039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.431 Γ— 10¹⁰⁰(101-digit number)
54313864690375515750…64634126806971054079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.086 Γ— 10¹⁰¹(102-digit number)
10862772938075103150…29268253613942108159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.172 Γ— 10¹⁰¹(102-digit number)
21725545876150206300…58536507227884216319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.345 Γ— 10¹⁰¹(102-digit number)
43451091752300412600…17073014455768432639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.690 Γ— 10¹⁰¹(102-digit number)
86902183504600825201…34146028911536865279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.738 Γ— 10¹⁰²(103-digit number)
17380436700920165040…68292057823073730559
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:57,699,149 XPMΒ·at block #6,806,879 Β· updates every 60s
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