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Block #2,259,614

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/20/2017, 3:25:47 AM Β· Difficulty 10.9520 Β· 4,584,146 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a4ca6c1642b433447fb3e1c8dacd33ed341d4df5a748f35a57b59e6a95aa4c81
View on Chainz β†—

Height

#2,259,614

Difficulty

10.952005

Transactions

1

Size

201 B

Version

2

Bits

0af3b69d

Nonce

2,115,907,185

Timestamp

8/20/2017, 3:25:47 AM

Confirmations

4,584,146

Mined by

⛏️ P2SHAWCcprsHwd4Dpvfz9XXUjt1yF2Z5MDcL1T

Merkle Root

a2809e2397d156ed4088e3be4bdf11d2c7c6905c656375ff13682d6aec9bce24
Transactions (1)
Coinbasea2809e2397d156…682d6aec9bce24
1 in β†’ 1 out8.3200 XPM110 B
AWCcprsH…Z5MDcL1T
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.

2.142 Γ— 10⁹⁷(98-digit number)
21426910135754606092…25321677272017326079
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
2.142 Γ— 10⁹⁷(98-digit number)
21426910135754606092…25321677272017326079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.285 Γ— 10⁹⁷(98-digit number)
42853820271509212185…50643354544034652159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.570 Γ— 10⁹⁷(98-digit number)
85707640543018424370…01286709088069304319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.714 Γ— 10⁹⁸(99-digit number)
17141528108603684874…02573418176138608639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.428 Γ— 10⁹⁸(99-digit number)
34283056217207369748…05146836352277217279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.856 Γ— 10⁹⁸(99-digit number)
68566112434414739496…10293672704554434559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.371 Γ— 10⁹⁹(100-digit number)
13713222486882947899…20587345409108869119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.742 Γ— 10⁹⁹(100-digit number)
27426444973765895798…41174690818217738239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.485 Γ— 10⁹⁹(100-digit number)
54852889947531791597…82349381636435476479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.097 Γ— 10¹⁰⁰(101-digit number)
10970577989506358319…64698763272870952959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.194 Γ— 10¹⁰⁰(101-digit number)
21941155979012716638…29397526545741905919
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:57,994,452 XPMΒ·at block #6,843,759 Β· updates every 60s
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