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Block #2,244,109

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 8/9/2017, 4:32:48 PM Β· Difficulty 10.9470 Β· 4,594,487 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
874737fbfc2ebae40a210998f1f35030172d9c197d40f600c5d089bd0ae27cd5
View on Chainz β†—

Height

#2,244,109

Difficulty

10.947046

Transactions

2

Size

34.66 KB

Version

2

Bits

0af27199

Nonce

1,295,656,370

Timestamp

8/9/2017, 4:32:48 PM

Confirmations

4,594,487

Mined by

⛏️ P2SHAf4FiC84DmSC2aWFtepDpRbkKRSjz2WFz3

Merkle Root

05d4a20d4e16387d5af9499235c02696c07fcd70ec4fc837beed5ed1080b0ced
Transactions (2)
Coinbasecc79f2a1644a0d…6383a1d72a3373
1 in β†’ 1 out9.0600 XPM109 B
Af4FiC84…Sjz2WFz3
242e2fdaec8e7f…76aed4c18555ab
238 in β†’ 2 out2970.0102 XPM34.46 KB
ALemuze2…hahGfReZAaJdN68U…29ZgLz2p
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.

1.025 Γ— 10⁹⁡(96-digit number)
10251634580270829933…39693090515546871681
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
1.025 Γ— 10⁹⁡(96-digit number)
10251634580270829933…39693090515546871681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.050 Γ— 10⁹⁡(96-digit number)
20503269160541659867…79386181031093743361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.100 Γ— 10⁹⁡(96-digit number)
41006538321083319734…58772362062187486721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
8.201 Γ— 10⁹⁡(96-digit number)
82013076642166639468…17544724124374973441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.640 Γ— 10⁹⁢(97-digit number)
16402615328433327893…35089448248749946881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.280 Γ— 10⁹⁢(97-digit number)
32805230656866655787…70178896497499893761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.561 Γ— 10⁹⁢(97-digit number)
65610461313733311574…40357792994999787521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.312 Γ— 10⁹⁷(98-digit number)
13122092262746662314…80715585989999575041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.624 Γ— 10⁹⁷(98-digit number)
26244184525493324629…61431171979999150081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.248 Γ— 10⁹⁷(98-digit number)
52488369050986649259…22862343959998300161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.049 Γ— 10⁹⁸(99-digit number)
10497673810197329851…45724687919996600321
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,953,055 XPMΒ·at block #6,838,595 Β· updates every 60s
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