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Block #65,300

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2013, 11:37:16 AM Β· Difficulty 8.9838 Β· 6,750,756 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
79e56a870107ac1f62370ab0f708c5fff07043483bc5f2261b3c80f80944379c
View on Chainz β†—

Height

#65,300

Difficulty

8.983806

Transactions

1

Size

201 B

Version

2

Bits

08fbdab4

Nonce

694

Timestamp

7/19/2013, 11:37:16 AM

Confirmations

6,750,756

Mined by

⛏️ P2SHAK1JUKWLjkgQU8N3MsSKyKCPeAoPR4rN5o

Merkle Root

8edf3cbc2828008291fe77873fe95caf1bf07d2b49703b2371937d8e15d160d3
Transactions (1)
Coinbase8edf3cbc282800…937d8e15d160d3
1 in β†’ 1 out12.3700 XPM110 B
AK1JUKWL…oPR4rN5o
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.

1.469 Γ— 10⁹⁸(99-digit number)
14693581090102518201…83097042610985810811
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
1.469 Γ— 10⁹⁸(99-digit number)
14693581090102518201…83097042610985810811
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.938 Γ— 10⁹⁸(99-digit number)
29387162180205036402…66194085221971621621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.877 Γ— 10⁹⁸(99-digit number)
58774324360410072804…32388170443943243241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.175 Γ— 10⁹⁹(100-digit number)
11754864872082014560…64776340887886486481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.350 Γ— 10⁹⁹(100-digit number)
23509729744164029121…29552681775772972961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.701 Γ— 10⁹⁹(100-digit number)
47019459488328058243…59105363551545945921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.403 Γ— 10⁹⁹(100-digit number)
94038918976656116486…18210727103091891841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.880 Γ— 10¹⁰⁰(101-digit number)
18807783795331223297…36421454206183783681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.761 Γ— 10¹⁰⁰(101-digit number)
37615567590662446594…72842908412367567361
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:57,772,563 XPMΒ·at block #6,816,055 Β· updates every 60s
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