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Block #2,275,833

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/31/2017, 5:15:37 AM Β· Difficulty 10.9550 Β· 4,564,426 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
109400f276132f714b10fed180ecc80aa54159084d7371017efc1a8fa2b8e1d0
View on Chainz β†—

Height

#2,275,833

Difficulty

10.954978

Transactions

2

Size

426 B

Version

2

Bits

0af47972

Nonce

1,425,060,872

Timestamp

8/31/2017, 5:15:37 AM

Confirmations

4,564,426

Mined by

⛏️ P2SHAVg8gsUZigjiFLktc5zTcjesQzq7PbzGBE

Merkle Root

35930f2d10a4e84cefa84e71eff2cb21a621a2eafcfd4db704a08d4a46070373
Transactions (2)
Coinbase5b7369704100b5…58760c234e48c7
1 in β†’ 1 out8.3300 XPM110 B
AVg8gsUZ…q7PbzGBE
57c77a2d8ec669…186b16483d8acf
1 in β†’ 2 out2771.9800 XPM226 B
APsXZFG8…4GQAm6NGAKfa7uit…MH3HUNwy
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.

8.178 Γ— 10⁹⁡(96-digit number)
81785936659598748008…41510444952245359361
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
8.178 Γ— 10⁹⁡(96-digit number)
81785936659598748008…41510444952245359361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.635 Γ— 10⁹⁢(97-digit number)
16357187331919749601…83020889904490718721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.271 Γ— 10⁹⁢(97-digit number)
32714374663839499203…66041779808981437441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.542 Γ— 10⁹⁢(97-digit number)
65428749327678998406…32083559617962874881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.308 Γ— 10⁹⁷(98-digit number)
13085749865535799681…64167119235925749761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.617 Γ— 10⁹⁷(98-digit number)
26171499731071599362…28334238471851499521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.234 Γ— 10⁹⁷(98-digit number)
52342999462143198725…56668476943702999041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.046 Γ— 10⁹⁸(99-digit number)
10468599892428639745…13336953887405998081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.093 Γ— 10⁹⁸(99-digit number)
20937199784857279490…26673907774811996161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.187 Γ— 10⁹⁸(99-digit number)
41874399569714558980…53347815549623992321
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:57,966,385 XPMΒ·at block #6,840,258 Β· updates every 60s
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