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Block #582,062

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/9/2014, 7:54:31 AM Β· Difficulty 10.9608 Β· 6,213,303 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
084bf75827d165f5a0f60187e52481fcc6362e3c4aa2c2a541a221d2834ea6d4
View on Chainz β†—

Height

#582,062

Difficulty

10.960794

Transactions

1

Size

731 B

Version

2

Bits

0af5f698

Nonce

7,433

Timestamp

6/9/2014, 7:54:31 AM

Confirmations

6,213,303

Mined by

⛏️ aSh5AJzWx2VDShfKP9pKK3jZqTbn4sj4ZSMit5

Merkle Root

69b102f300a4d7f63447a5d8be6836feae78a2244646f8d84346bb2efac836fe
Transactions (1)
Coinbase69b102f300a4d7…46bb2efac836fe
1 in β†’ 17 out8.3100 XPM641 B
AJzWx2VD…j4ZSMit5AQv2iMwd…EFna22eeAJtNW28X…Syb4Ph5jAQyr8Lw3…hs4nt3PnAJtsGkR4…BuZ5GKQN
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.

1.746 Γ— 10⁹⁡(96-digit number)
17462129228040306862…18254604273712299959
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
1.746 Γ— 10⁹⁡(96-digit number)
17462129228040306862…18254604273712299959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.492 Γ— 10⁹⁡(96-digit number)
34924258456080613725…36509208547424599919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.984 Γ— 10⁹⁡(96-digit number)
69848516912161227451…73018417094849199839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.396 Γ— 10⁹⁢(97-digit number)
13969703382432245490…46036834189698399679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.793 Γ— 10⁹⁢(97-digit number)
27939406764864490980…92073668379396799359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.587 Γ— 10⁹⁢(97-digit number)
55878813529728981960…84147336758793598719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.117 Γ— 10⁹⁷(98-digit number)
11175762705945796392…68294673517587197439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.235 Γ— 10⁹⁷(98-digit number)
22351525411891592784…36589347035174394879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.470 Γ— 10⁹⁷(98-digit number)
44703050823783185568…73178694070348789759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.940 Γ— 10⁹⁷(98-digit number)
89406101647566371137…46357388140697579519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.788 Γ— 10⁹⁸(99-digit number)
17881220329513274227…92714776281395159039
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:57,606,976 XPMΒ·at block #6,795,364 Β· updates every 60s
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