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Block #27,826

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/13/2013, 10:12:02 AM Β· Difficulty 7.9801 Β· 6,790,103 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4d22be6599bd6d4138ad389e62d23c67acfdadd1af46538d3c7d6a58d2960bfa
View on Chainz β†—

Height

#27,826

Difficulty

7.980072

Transactions

1

Size

201 B

Version

2

Bits

07fae608

Nonce

549

Timestamp

7/13/2013, 10:12:02 AM

Confirmations

6,790,103

Mined by

⛏️ P2SHAXciC8HNS9S5P5rEuP4DvtNMFMEX3Zpc3u

Merkle Root

ac65fd8dfaa6a0a61953a2e573fe313e649b390ddc3eeb900bf564e59b9492e4
Transactions (1)
Coinbaseac65fd8dfaa6a0…f564e59b9492e4
1 in β†’ 1 out15.6800 XPM108 B
AXciC8HN…EX3Zpc3u
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.

8.217 Γ— 10¹⁰²(103-digit number)
82176200108230723259…73226247188928149391
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
8.217 Γ— 10¹⁰²(103-digit number)
82176200108230723259…73226247188928149391
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.643 Γ— 10¹⁰³(104-digit number)
16435240021646144651…46452494377856298781
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.287 Γ— 10¹⁰³(104-digit number)
32870480043292289303…92904988755712597561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.574 Γ— 10¹⁰³(104-digit number)
65740960086584578607…85809977511425195121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.314 Γ— 10¹⁰⁴(105-digit number)
13148192017316915721…71619955022850390241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.629 Γ— 10¹⁰⁴(105-digit number)
26296384034633831442…43239910045700780481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.259 Γ— 10¹⁰⁴(105-digit number)
52592768069267662885…86479820091401560961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.051 Γ— 10¹⁰⁡(106-digit number)
10518553613853532577…72959640182803121921
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,787,499 XPMΒ·at block #6,817,928 Β· updates every 60s
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