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Block #2,645,766

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/3/2018, 1:33:30 AM Β· Difficulty 11.7383 Β· 4,194,317 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aa89929114a0661480f2ac40524bf786ef826fb9561b0cf2c6ed93d391ae532f
View on Chainz β†—

Height

#2,645,766

Difficulty

11.738321

Transactions

2

Size

573 B

Version

2

Bits

0bbd029c

Nonce

643,942,296

Timestamp

5/3/2018, 1:33:30 AM

Confirmations

4,194,317

Mined by

⛏️ P2SHARWQjRhbMyK1yZJGzZLpXZHxBz4cEiE3dB

Merkle Root

80f24d38a407056232f3f8b53d6d979396b218b31f86c6581a560134231b57b2
Transactions (2)
Coinbasefc89a916572078…00a7c33a21094f
1 in β†’ 1 out7.2600 XPM110 B
ARWQjRhb…4cEiE3dB
7f0aab74338642…b600403985f21d
2 in β†’ 2 out203.1385 XPM373 B
AeA81nnA…qmozy4QjASC9um3f…YLq9NmQu
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.

7.129 Γ— 10⁹⁴(95-digit number)
71290182194008062068…82465867004392857919
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
7.129 Γ— 10⁹⁴(95-digit number)
71290182194008062068…82465867004392857919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.425 Γ— 10⁹⁡(96-digit number)
14258036438801612413…64931734008785715839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.851 Γ— 10⁹⁡(96-digit number)
28516072877603224827…29863468017571431679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.703 Γ— 10⁹⁡(96-digit number)
57032145755206449654…59726936035142863359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.140 Γ— 10⁹⁢(97-digit number)
11406429151041289930…19453872070285726719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.281 Γ— 10⁹⁢(97-digit number)
22812858302082579861…38907744140571453439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.562 Γ— 10⁹⁢(97-digit number)
45625716604165159723…77815488281142906879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.125 Γ— 10⁹⁢(97-digit number)
91251433208330319447…55630976562285813759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.825 Γ— 10⁹⁷(98-digit number)
18250286641666063889…11261953124571627519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.650 Γ— 10⁹⁷(98-digit number)
36500573283332127779…22523906249143255039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.300 Γ— 10⁹⁷(98-digit number)
73001146566664255558…45047812498286510079
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:57,964,972 XPMΒ·at block #6,840,082 Β· updates every 60s
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