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Block #72,318

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/20/2013, 11:25:36 PM Β· Difficulty 8.9940 Β· 6,727,047 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d517f89a6101dfa619c6a2352dbbc57ccf39334ea0680e9a4ab0c535659030fb
View on Chainz β†—

Height

#72,318

Difficulty

8.993974

Transactions

1

Size

200 B

Version

2

Bits

08fe7510

Nonce

205

Timestamp

7/20/2013, 11:25:36 PM

Confirmations

6,727,047

Mined by

⛏️ P2SHAZDgU5ryLDBgQ43WTK1SQdESypdmcwdqVC

Merkle Root

ed22a3d0cc0bbc82888b7f164b124460137c92297d65cf644eb5f6ac341dee0b
Transactions (1)
Coinbaseed22a3d0cc0bbc…b5f6ac341dee0b
1 in β†’ 1 out12.3400 XPM110 B
AZDgU5ry…dmcwdqVC
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.

9.611 Γ— 10⁹⁴(95-digit number)
96112007824619920999…63491293856768532221
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
9.611 Γ— 10⁹⁴(95-digit number)
96112007824619920999…63491293856768532221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.922 Γ— 10⁹⁡(96-digit number)
19222401564923984199…26982587713537064441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.844 Γ— 10⁹⁡(96-digit number)
38444803129847968399…53965175427074128881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.688 Γ— 10⁹⁡(96-digit number)
76889606259695936799…07930350854148257761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.537 Γ— 10⁹⁢(97-digit number)
15377921251939187359…15860701708296515521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.075 Γ— 10⁹⁢(97-digit number)
30755842503878374719…31721403416593031041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.151 Γ— 10⁹⁢(97-digit number)
61511685007756749439…63442806833186062081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.230 Γ— 10⁹⁷(98-digit number)
12302337001551349887…26885613666372124161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.460 Γ— 10⁹⁷(98-digit number)
24604674003102699775…53771227332744248321
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:57,638,967 XPMΒ·at block #6,799,364 Β· updates every 60s
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