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Block #2,241,280

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/7/2017, 5:50:43 PM Β· Difficulty 10.9466 Β· 4,585,802 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
54c631bf9a8451bc9d7ad9b08b3e44d75292628640c8c7e94ba169cfc3818df0
View on Chainz β†—

Height

#2,241,280

Difficulty

10.946647

Transactions

2

Size

721 B

Version

2

Bits

0af2577c

Nonce

295,966,320

Timestamp

8/7/2017, 5:50:43 PM

Confirmations

4,585,802

Mined by

⛏️ P2SHAX35cjT7vbk4VT23TerJpHzZMXBW8XdvsL

Merkle Root

4f2d111f3fd5f9bc4823ccd5b5bd998301c424814f60a75fd621c8c67e092932
Transactions (2)
Coinbaseef284d45ae31b7…e80d0881409d6f
1 in β†’ 1 out8.3400 XPM110 B
AX35cjT7…BW8XdvsL
bac55fcebf4151…8fc06dae09b6dd
3 in β†’ 2 out170.0051 XPM521 B
AMfu2XSP…9SVjqYfeAd27Nz4m…CCnTdvs6
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.

1.027 Γ— 10⁹⁡(96-digit number)
10278984010616708455…60126920405981902081
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
1.027 Γ— 10⁹⁡(96-digit number)
10278984010616708455…60126920405981902081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.055 Γ— 10⁹⁡(96-digit number)
20557968021233416910…20253840811963804161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.111 Γ— 10⁹⁡(96-digit number)
41115936042466833821…40507681623927608321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.223 Γ— 10⁹⁡(96-digit number)
82231872084933667643…81015363247855216641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.644 Γ— 10⁹⁢(97-digit number)
16446374416986733528…62030726495710433281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.289 Γ— 10⁹⁢(97-digit number)
32892748833973467057…24061452991420866561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.578 Γ— 10⁹⁢(97-digit number)
65785497667946934114…48122905982841733121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.315 Γ— 10⁹⁷(98-digit number)
13157099533589386822…96245811965683466241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.631 Γ— 10⁹⁷(98-digit number)
26314199067178773645…92491623931366932481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.262 Γ— 10⁹⁷(98-digit number)
52628398134357547291…84983247862733864961
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:57,860,841 XPMΒ·at block #6,827,081 Β· updates every 60s
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