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Block #2,556,204

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/9/2018, 12:25:07 AM Β· Difficulty 10.9911 Β· 4,275,952 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3bc13db36ed0f8c7667a0017b2b66af4966eb926c2d1c73dd85a7f03bf3b7d1b
View on Chainz β†—

Height

#2,556,204

Difficulty

10.991108

Transactions

2

Size

1.54 KB

Version

2

Bits

0afdb945

Nonce

104,977,202

Timestamp

3/9/2018, 12:25:07 AM

Confirmations

4,275,952

Mined by

⛏️ P2SHAbGngT8JL9i5baLAoZmxiCrGsHYxxzLTkm

Merkle Root

ca1922335c585397b2f479638721960ce81f7ef08bb2b607b113e8967efb9575
Transactions (2)
Coinbased4556e0caae443…1d9ca3aed274d7
1 in β†’ 1 out8.2800 XPM109 B
AbGngT8J…YxxzLTkm
fb836c2aac8134…1bf1a1d5a32262
9 in β†’ 1 out35.9800 XPM1.34 KB
ASEhqc6y…uiLW8tms
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.

8.829 Γ— 10⁹³(94-digit number)
88292794011403363118…69109777187710711041
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
8.829 Γ— 10⁹³(94-digit number)
88292794011403363118…69109777187710711041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.765 Γ— 10⁹⁴(95-digit number)
17658558802280672623…38219554375421422081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.531 Γ— 10⁹⁴(95-digit number)
35317117604561345247…76439108750842844161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.063 Γ— 10⁹⁴(95-digit number)
70634235209122690494…52878217501685688321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.412 Γ— 10⁹⁡(96-digit number)
14126847041824538098…05756435003371376641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.825 Γ— 10⁹⁡(96-digit number)
28253694083649076197…11512870006742753281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.650 Γ— 10⁹⁡(96-digit number)
56507388167298152395…23025740013485506561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.130 Γ— 10⁹⁢(97-digit number)
11301477633459630479…46051480026971013121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.260 Γ— 10⁹⁢(97-digit number)
22602955266919260958…92102960053942026241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.520 Γ— 10⁹⁢(97-digit number)
45205910533838521916…84205920107884052481
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:57,901,387 XPMΒ·at block #6,832,155 Β· updates every 60s
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