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Block #2,237,324

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/5/2017, 12:43:22 AM Β· Difficulty 10.9460 Β· 4,604,504 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4ace6bfa78fbe515ca65965dabf38ee9585fea83df0df73e137009c3f217b76e
View on Chainz β†—

Height

#2,237,324

Difficulty

10.946010

Transactions

2

Size

722 B

Version

2

Bits

0af22dae

Nonce

296,898,886

Timestamp

8/5/2017, 12:43:22 AM

Confirmations

4,604,504

Mined by

⛏️ P2SHAKG6HhoQ7cuoFvE7ZGmJB4G8R3FsEbWsGK

Merkle Root

7abca7eaffa1d310d6eb409d814736c1176ce5432723d8db3b1e713e45579644
Transactions (2)
Coinbase507f4692ce5e87…576285e7e5f661
1 in β†’ 1 out8.3400 XPM109 B
AKG6HhoQ…FsEbWsGK
34d06267ae5e24…0ad6401376a88a
3 in β†’ 2 out1463.7884 XPM523 B
AJJDu76n…RhqNwfHfAesaHg9U…6tjRExna
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.

1.627 Γ— 10⁹⁡(96-digit number)
16276426475564753084…04709975451437039281
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
1.627 Γ— 10⁹⁡(96-digit number)
16276426475564753084…04709975451437039281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.255 Γ— 10⁹⁡(96-digit number)
32552852951129506168…09419950902874078561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.510 Γ— 10⁹⁡(96-digit number)
65105705902259012337…18839901805748157121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.302 Γ— 10⁹⁢(97-digit number)
13021141180451802467…37679803611496314241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.604 Γ— 10⁹⁢(97-digit number)
26042282360903604934…75359607222992628481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
5.208 Γ— 10⁹⁢(97-digit number)
52084564721807209869…50719214445985256961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.041 Γ— 10⁹⁷(98-digit number)
10416912944361441973…01438428891970513921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.083 Γ— 10⁹⁷(98-digit number)
20833825888722883947…02876857783941027841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
4.166 Γ— 10⁹⁷(98-digit number)
41667651777445767895…05753715567882055681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
8.333 Γ— 10⁹⁷(98-digit number)
83335303554891535791…11507431135764111361
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,978,997 XPMΒ·at block #6,841,827 Β· updates every 60s
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