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Block #72,615

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/21/2013, 1:14:56 AM Β· Difficulty 8.9942 Β· 6,723,877 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
5fd32436f4556c31eef50e1952ee2a862a7f6013010b846ca3f96b7f9a1f5a10
View on Chainz β†—

Height

#72,615

Difficulty

8.994202

Transactions

1

Size

199 B

Version

2

Bits

08fe840a

Nonce

719

Timestamp

7/21/2013, 1:14:56 AM

Confirmations

6,723,877

Mined by

⛏️ P2SHAN2RVhNyAZ7aBqdG9weGSmXTCb6D8axJNU

Merkle Root

a3bda77d47a64b65f8d38c23ab17712a7c62663fb235e5096a7fff146441f310
Transactions (1)
Coinbasea3bda77d47a64b…7fff146441f310
1 in β†’ 1 out12.3400 XPM110 B
AN2RVhNy…6D8axJNU
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.

5.180 Γ— 10⁹²(93-digit number)
51807934315833885421…26231528317004657761
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
5.180 Γ— 10⁹²(93-digit number)
51807934315833885421…26231528317004657761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.036 Γ— 10⁹³(94-digit number)
10361586863166777084…52463056634009315521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.072 Γ— 10⁹³(94-digit number)
20723173726333554168…04926113268018631041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
4.144 Γ— 10⁹³(94-digit number)
41446347452667108337…09852226536037262081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
8.289 Γ— 10⁹³(94-digit number)
82892694905334216674…19704453072074524161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.657 Γ— 10⁹⁴(95-digit number)
16578538981066843334…39408906144149048321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.315 Γ— 10⁹⁴(95-digit number)
33157077962133686669…78817812288298096641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.631 Γ— 10⁹⁴(95-digit number)
66314155924267373339…57635624576596193281
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 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 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,615,935 XPMΒ·at block #6,796,491 Β· updates every 60s
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