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Block #75,664

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 5:57:23 PM Β· Difficulty 9.0289 Β· 6,720,854 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
860b2cad13deb1066ebde3570a94bdfec1d64b23552cae7f211776fda98f7374
View on Chainz β†—

Height

#75,664

Difficulty

9.028894

Transactions

1

Size

201 B

Version

2

Bits

09076599

Nonce

183

Timestamp

7/21/2013, 5:57:23 PM

Confirmations

6,720,854

Mined by

⛏️ P2SHAcBadmkptMo3EwP8cg9ZUyqvJMGmhL921o

Merkle Root

e37da46daf42ef54ea743a01a143841c222b8fb5014dcde129cb247b24d0eafc
Transactions (1)
Coinbasee37da46daf42ef…cb247b24d0eafc
1 in β†’ 1 out12.2500 XPM110 B
AcBadmkp…GmhL921o
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.

1.181 Γ— 10⁹⁢(97-digit number)
11813831046638140643…70009700206170397711
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
1.181 Γ— 10⁹⁢(97-digit number)
11813831046638140643…70009700206170397711
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.362 Γ— 10⁹⁢(97-digit number)
23627662093276281287…40019400412340795421
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.725 Γ— 10⁹⁢(97-digit number)
47255324186552562575…80038800824681590841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.451 Γ— 10⁹⁢(97-digit number)
94510648373105125150…60077601649363181681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.890 Γ— 10⁹⁷(98-digit number)
18902129674621025030…20155203298726363361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.780 Γ— 10⁹⁷(98-digit number)
37804259349242050060…40310406597452726721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.560 Γ— 10⁹⁷(98-digit number)
75608518698484100120…80620813194905453441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.512 Γ— 10⁹⁸(99-digit number)
15121703739696820024…61241626389810906881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.024 Γ— 10⁹⁸(99-digit number)
30243407479393640048…22483252779621813761
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 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 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,616,141 XPMΒ·at block #6,796,517 Β· updates every 60s
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