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Block #78,582

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/22/2013, 11:57:57 PM Β· Difficulty 9.2226 Β· 6,720,730 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
22821af394d1a14c03961696d86ac2a6a390b8d9703d5d523c510bab3929a2d4
View on Chainz β†—

Height

#78,582

Difficulty

9.222585

Transactions

1

Size

200 B

Version

2

Bits

0938fb57

Nonce

524

Timestamp

7/22/2013, 11:57:57 PM

Confirmations

6,720,730

Mined by

⛏️ P2SHAbmC177FbWsA3xjDrM8MdR2hvjpomdGgdX

Merkle Root

7499884354ab25a005cace49b05204f8b0b0ef5f2fd51d76611a0219abd55647
Transactions (1)
Coinbase7499884354ab25…1a0219abd55647
1 in β†’ 1 out11.7400 XPM110 B
AbmC177F…pomdGgdX
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.

7.105 Γ— 10⁹⁴(95-digit number)
71058058908132546011…86238394676553776199
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
7.105 Γ— 10⁹⁴(95-digit number)
71058058908132546011…86238394676553776199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.421 Γ— 10⁹⁡(96-digit number)
14211611781626509202…72476789353107552399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.842 Γ— 10⁹⁡(96-digit number)
28423223563253018404…44953578706215104799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.684 Γ— 10⁹⁡(96-digit number)
56846447126506036809…89907157412430209599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.136 Γ— 10⁹⁢(97-digit number)
11369289425301207361…79814314824860419199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.273 Γ— 10⁹⁢(97-digit number)
22738578850602414723…59628629649720838399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.547 Γ— 10⁹⁢(97-digit number)
45477157701204829447…19257259299441676799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.095 Γ— 10⁹⁢(97-digit number)
90954315402409658894…38514518598883353599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.819 Γ— 10⁹⁷(98-digit number)
18190863080481931778…77029037197766707199
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:57,638,543 XPMΒ·at block #6,799,311 Β· updates every 60s
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