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Block #2,643,501

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/2/2018, 3:14:34 AM Β· Difficulty 11.6854 Β· 4,199,539 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9c3b9e4c5e3bcffd444000f5aa4d21be3774e1a9159be8a8371b0041535c6ba2
View on Chainz β†—

Height

#2,643,501

Difficulty

11.685376

Transactions

1

Size

199 B

Version

2

Bits

0baf74d1

Nonce

441,584,838

Timestamp

5/2/2018, 3:14:34 AM

Confirmations

4,199,539

Mined by

⛏️ P2SHAMCRj91ZmQNk2VyytQZPSTxLPxaPWZcDBf

Merkle Root

698b2eb72a9d3e81b1d6384c0d0fd8c38ae10e2105010c9f3da44199946a8378
Transactions (1)
Coinbase698b2eb72a9d3e…a44199946a8378
1 in β†’ 1 out7.3100 XPM110 B
AMCRj91Z…aPWZcDBf
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.

2.363 Γ— 10⁹²(93-digit number)
23635579061541758409…89243852927960397839
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
2.363 Γ— 10⁹²(93-digit number)
23635579061541758409…89243852927960397839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.727 Γ— 10⁹²(93-digit number)
47271158123083516818…78487705855920795679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.454 Γ— 10⁹²(93-digit number)
94542316246167033636…56975411711841591359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.890 Γ— 10⁹³(94-digit number)
18908463249233406727…13950823423683182719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.781 Γ— 10⁹³(94-digit number)
37816926498466813454…27901646847366365439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.563 Γ— 10⁹³(94-digit number)
75633852996933626909…55803293694732730879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.512 Γ— 10⁹⁴(95-digit number)
15126770599386725381…11606587389465461759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.025 Γ— 10⁹⁴(95-digit number)
30253541198773450763…23213174778930923519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.050 Γ— 10⁹⁴(95-digit number)
60507082397546901527…46426349557861847039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.210 Γ— 10⁹⁡(96-digit number)
12101416479509380305…92852699115723694079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.420 Γ— 10⁹⁡(96-digit number)
24202832959018760610…85705398231447388159
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:57,988,677 XPMΒ·at block #6,843,039 Β· updates every 60s
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