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Block #36,275

1CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/14/2013, 9:12:00 AM Β· Difficulty 7.9952 Β· 6,780,585 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dcd628a008db592013cbc47a148e29cee4428fd575b0e7e5328417042179c320
View on Chainz β†—

Height

#36,275

Difficulty

7.995231

Transactions

1

Size

200 B

Version

2

Bits

07fec776

Nonce

10

Timestamp

7/14/2013, 9:12:00 AM

Confirmations

6,780,585

Mined by

⛏️ P2SHAPVhiwbSUWhvbmUr8W7P6XSJeXKgb3baPW

Merkle Root

dc36e5185bd1788829e5e99cfa442aaa56de58c1c5451ab8be18e99bec1d7464
Transactions (1)
Coinbasedc36e5185bd178…18e99bec1d7464
1 in β†’ 1 out15.6200 XPM109 B
APVhiwbS…Kgb3baPW
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.

8.161 Γ— 10⁹⁷(98-digit number)
81618549753595393191…94642724806204448499
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
8.161 Γ— 10⁹⁷(98-digit number)
81618549753595393191…94642724806204448499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.632 Γ— 10⁹⁸(99-digit number)
16323709950719078638…89285449612408896999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.264 Γ— 10⁹⁸(99-digit number)
32647419901438157276…78570899224817793999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.529 Γ— 10⁹⁸(99-digit number)
65294839802876314553…57141798449635587999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.305 Γ— 10⁹⁹(100-digit number)
13058967960575262910…14283596899271175999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.611 Γ— 10⁹⁹(100-digit number)
26117935921150525821…28567193798542351999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.223 Γ— 10⁹⁹(100-digit number)
52235871842301051642…57134387597084703999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.044 Γ— 10¹⁰⁰(101-digit number)
10447174368460210328…14268775194169407999
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 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 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,778,923 XPMΒ·at block #6,816,859 Β· updates every 60s
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