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Block #2,646,329

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/3/2018, 7:40:21 AM Β· Difficulty 11.7483 Β· 4,196,985 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
50b288e1ff3f4e03db1b1f701a12a105e9b464af321b0880c4e80b808091d219
View on Chainz β†—

Height

#2,646,329

Difficulty

11.748284

Transactions

1

Size

200 B

Version

2

Bits

0bbf8f89

Nonce

336,780,873

Timestamp

5/3/2018, 7:40:21 AM

Confirmations

4,196,985

Mined by

⛏️ P2SHAWqbnsmFSEeJJ4SJ1SftA1ApEaLTFpNFtj

Merkle Root

25b54b9a472ef1e51dbc3c6645755dcff8de634358bca02f26fa6f7b35525e82
Transactions (1)
Coinbase25b54b9a472ef1…fa6f7b35525e82
1 in β†’ 1 out7.2300 XPM110 B
AWqbnsmF…LTFpNFtj
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.

3.474 Γ— 10⁹⁡(96-digit number)
34741476223293128098…83517478712301345279
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.474 Γ— 10⁹⁡(96-digit number)
34741476223293128098…83517478712301345279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.948 Γ— 10⁹⁡(96-digit number)
69482952446586256196…67034957424602690559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.389 Γ— 10⁹⁢(97-digit number)
13896590489317251239…34069914849205381119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.779 Γ— 10⁹⁢(97-digit number)
27793180978634502478…68139829698410762239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.558 Γ— 10⁹⁢(97-digit number)
55586361957269004957…36279659396821524479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.111 Γ— 10⁹⁷(98-digit number)
11117272391453800991…72559318793643048959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.223 Γ— 10⁹⁷(98-digit number)
22234544782907601983…45118637587286097919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.446 Γ— 10⁹⁷(98-digit number)
44469089565815203966…90237275174572195839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.893 Γ— 10⁹⁷(98-digit number)
88938179131630407932…80474550349144391679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.778 Γ— 10⁹⁸(99-digit number)
17787635826326081586…60949100698288783359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.557 Γ— 10⁹⁸(99-digit number)
35575271652652163172…21898201396577566719
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,990,870 XPMΒ·at block #6,843,313 Β· updates every 60s
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