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Block #2,532,870

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/22/2018, 4:44:29 AM Β· Difficulty 10.9860 Β· 4,309,406 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
37b0d65582786319b256c0997f512966c72c13cb89126067746637f8cc7d711d
View on Chainz β†—

Height

#2,532,870

Difficulty

10.985983

Transactions

2

Size

686 B

Version

2

Bits

0afc695d

Nonce

1,218,693,875

Timestamp

2/22/2018, 4:44:29 AM

Confirmations

4,309,406

Mined by

⛏️ P2SHAVXodaR9XaT4B1kq35HWQqvwVJPXgU1BBD

Merkle Root

fd83db37149868ddc154704ede729a2f3e991c282c4a933e1e6ba24f74431dd2
Transactions (2)
Coinbase2c9927494a5bad…f996d53b7ba43e
1 in β†’ 1 out8.2800 XPM109 B
AVXodaR9…PXgU1BBD
5bc12c18c51602…cea27867aa0993
3 in β†’ 1 out8999.9900 XPM487 B
AT1bUu6o…owSzCB5o
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.

7.249 Γ— 10⁹³(94-digit number)
72490886168316958570…46480761258806973921
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
7.249 Γ— 10⁹³(94-digit number)
72490886168316958570…46480761258806973921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.449 Γ— 10⁹⁴(95-digit number)
14498177233663391714…92961522517613947841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.899 Γ— 10⁹⁴(95-digit number)
28996354467326783428…85923045035227895681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.799 Γ— 10⁹⁴(95-digit number)
57992708934653566856…71846090070455791361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.159 Γ— 10⁹⁡(96-digit number)
11598541786930713371…43692180140911582721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.319 Γ— 10⁹⁡(96-digit number)
23197083573861426742…87384360281823165441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.639 Γ— 10⁹⁡(96-digit number)
46394167147722853484…74768720563646330881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.278 Γ— 10⁹⁡(96-digit number)
92788334295445706969…49537441127292661761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.855 Γ— 10⁹⁢(97-digit number)
18557666859089141393…99074882254585323521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.711 Γ— 10⁹⁢(97-digit number)
37115333718178282787…98149764509170647041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
7.423 Γ— 10⁹⁢(97-digit number)
74230667436356565575…96299529018341294081
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:57,982,609 XPMΒ·at block #6,842,275 Β· updates every 60s
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