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Block #75,350

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 3:59:33 PM Β· Difficulty 8.9961 Β· 6,730,316 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e535b8598ba66cf0408995d44f6de0386f14250c1aef76141b43b6df7851902c
View on Chainz β†—

Height

#75,350

Difficulty

8.996055

Transactions

1

Size

200 B

Version

2

Bits

08fefd71

Nonce

156

Timestamp

7/21/2013, 3:59:33 PM

Confirmations

6,730,316

Mined by

⛏️ P2SHANey87HKeHbF7P31ach44cVFqNMGUx5bYr

Merkle Root

8d041ea5fa9b08f6bc8d36b6165c96e1e423028d361dd3823081523b25c36864
Transactions (1)
Coinbase8d041ea5fa9b08…81523b25c36864
1 in β†’ 1 out12.3400 XPM110 B
ANey87HK…MGUx5bYr
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.

3.864 Γ— 10⁹³(94-digit number)
38640336039016937114…27759873868752361111
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
3.864 Γ— 10⁹³(94-digit number)
38640336039016937114…27759873868752361111
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.728 Γ— 10⁹³(94-digit number)
77280672078033874229…55519747737504722221
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.545 Γ— 10⁹⁴(95-digit number)
15456134415606774845…11039495475009444441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.091 Γ— 10⁹⁴(95-digit number)
30912268831213549691…22078990950018888881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.182 Γ— 10⁹⁴(95-digit number)
61824537662427099383…44157981900037777761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.236 Γ— 10⁹⁡(96-digit number)
12364907532485419876…88315963800075555521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.472 Γ— 10⁹⁡(96-digit number)
24729815064970839753…76631927600151111041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.945 Γ— 10⁹⁡(96-digit number)
49459630129941679506…53263855200302222081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.891 Γ— 10⁹⁡(96-digit number)
98919260259883359013…06527710400604444161
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:57,689,406 XPMΒ·at block #6,805,665 Β· updates every 60s
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