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Block #64,243

2CCLength 8β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/19/2013, 6:29:23 AM Β· Difficulty 8.9812 Β· 6,730,574 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
974c5679e448786a16849d831af1a3337c37c4f4024b662a97c65d74beb93fdc
View on Chainz β†—

Height

#64,243

Difficulty

8.981177

Transactions

2

Size

871 B

Version

2

Bits

08fb2e66

Nonce

316

Timestamp

7/19/2013, 6:29:23 AM

Confirmations

6,730,574

Mined by

⛏️ P2SHAbVS5YbT5fABxEmDfR2LnnffYt9JbXXApW

Merkle Root

5499287b1e7b1f7697adc80656b056b1e0b8483f1637f2d0a8b73c8c7fa0a926
Transactions (2)
Coinbase0608ecd20dfaf3…4b060592623743
1 in β†’ 1 out12.3900 XPM110 B
AbVS5YbT…9JbXXApW
def04a32fdc2c3…3b3eae14768187
4 in β†’ 2 out111.1135 XPM672 B
AWteuqJK…Anx6dakMARvyg4T3…nL3qDtAq
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.

9.040 Γ— 10⁹²(93-digit number)
90405056909104172333…33169537534080905621
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
9.040 Γ— 10⁹²(93-digit number)
90405056909104172333…33169537534080905621
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.808 Γ— 10⁹³(94-digit number)
18081011381820834466…66339075068161811241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.616 Γ— 10⁹³(94-digit number)
36162022763641668933…32678150136323622481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.232 Γ— 10⁹³(94-digit number)
72324045527283337867…65356300272647244961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.446 Γ— 10⁹⁴(95-digit number)
14464809105456667573…30712600545294489921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.892 Γ— 10⁹⁴(95-digit number)
28929618210913335146…61425201090588979841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.785 Γ— 10⁹⁴(95-digit number)
57859236421826670293…22850402181177959681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.157 Γ— 10⁹⁡(96-digit number)
11571847284365334058…45700804362355919361
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:57,602,583 XPMΒ·at block #6,794,816 Β· updates every 60s
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