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Block #84,387

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/26/2013, 7:16:38 PM Β· Difficulty 9.2717 Β· 6,719,197 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c1b42cbff53cb39a6a8d6dc17ca6e1146c245de9a98bf658707e00dfe34b62b4
View on Chainz β†—

Height

#84,387

Difficulty

9.271743

Transactions

2

Size

361 B

Version

2

Bits

094590f1

Nonce

1,194

Timestamp

7/26/2013, 7:16:38 PM

Confirmations

6,719,197

Mined by

⛏️ P2SHAc4cDzTHa1rmGYvE4Emkzx9wRFV5ctWvQ8

Merkle Root

6a84bc19a5000985fbea0c138ebce59411e6b63051fa053a5e97c046db894bb7
Transactions (2)
Coinbase0ac6ef1cd1f8c2…09bdebfd9e6377
1 in β†’ 1 out11.6300 XPM110 B
Ac4cDzTH…V5ctWvQ8
55057858b19544…4f0303c6cb38ba
1 in β†’ 1 out11.6700 XPM157 B
AGjPFuk8…G8AukLLa
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.

2.255 Γ— 10¹⁰⁡(106-digit number)
22553266991041577450…00899782068392702939
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
2.255 Γ— 10¹⁰⁡(106-digit number)
22553266991041577450…00899782068392702939
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.510 Γ— 10¹⁰⁡(106-digit number)
45106533982083154901…01799564136785405879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.021 Γ— 10¹⁰⁡(106-digit number)
90213067964166309803…03599128273570811759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.804 Γ— 10¹⁰⁢(107-digit number)
18042613592833261960…07198256547141623519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.608 Γ— 10¹⁰⁢(107-digit number)
36085227185666523921…14396513094283247039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.217 Γ— 10¹⁰⁢(107-digit number)
72170454371333047842…28793026188566494079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.443 Γ— 10¹⁰⁷(108-digit number)
14434090874266609568…57586052377132988159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.886 Γ— 10¹⁰⁷(108-digit number)
28868181748533219137…15172104754265976319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.773 Γ— 10¹⁰⁷(108-digit number)
57736363497066438274…30344209508531952639
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,672,707 XPMΒ·at block #6,803,583 Β· updates every 60s
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