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Block #529,294

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/7/2014, 4:07:42 AM Β· Difficulty 10.8894 Β· 6,284,940 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ef166cfe1688ddf6dc5d076cfd2b05cf047eb3793bfea4d2a06f97632b291c49
View on Chainz β†—

Height

#529,294

Difficulty

10.889449

Transactions

1

Size

208 B

Version

2

Bits

0ae3b2ee

Nonce

474,524,199

Timestamp

5/7/2014, 4:07:42 AM

Confirmations

6,284,940

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

da8a131cb7375742b231d83b0f7453b460e4cdded6e61335bd9640e2d35a75f2
Transactions (1)
Coinbaseda8a131cb73757…9640e2d35a75f2
1 in β†’ 1 out8.4200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.335 Γ— 10¹⁰⁰(101-digit number)
13351759038002786508…34318620284495155199
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
1.335 Γ— 10¹⁰⁰(101-digit number)
13351759038002786508…34318620284495155199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.670 Γ— 10¹⁰⁰(101-digit number)
26703518076005573017…68637240568990310399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.340 Γ— 10¹⁰⁰(101-digit number)
53407036152011146034…37274481137980620799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.068 Γ— 10¹⁰¹(102-digit number)
10681407230402229206…74548962275961241599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.136 Γ— 10¹⁰¹(102-digit number)
21362814460804458413…49097924551922483199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.272 Γ— 10¹⁰¹(102-digit number)
42725628921608916827…98195849103844966399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.545 Γ— 10¹⁰¹(102-digit number)
85451257843217833655…96391698207689932799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.709 Γ— 10¹⁰²(103-digit number)
17090251568643566731…92783396415379865599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.418 Γ— 10¹⁰²(103-digit number)
34180503137287133462…85566792830759731199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.836 Γ— 10¹⁰²(103-digit number)
68361006274574266924…71133585661519462399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.367 Γ— 10¹⁰³(104-digit number)
13672201254914853384…42267171323038924799
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:57,757,943 XPMΒ·at block #6,814,233 Β· updates every 60s
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