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Block #484,345

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/10/2014, 12:33:13 PM Β· Difficulty 10.5836 Β· 6,325,238 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
97ca5f702fdf31775773035692eb6805f1772674951f911d771a83cca86acfee
View on Chainz β†—

Height

#484,345

Difficulty

10.583550

Transactions

2

Size

1.14 KB

Version

2

Bits

0a95638b

Nonce

4,628,758

Timestamp

4/10/2014, 12:33:13 PM

Confirmations

6,325,238

Mined by

⛏️ P2SHAWZKhFPVUAKCJBEvJYh5mVX7UJB2AaxTqs

Merkle Root

0b43fb783c3381b3e0f1cb2784d5da3de76f8b328b0e72360f92cbf50ce09af2
Transactions (2)
Coinbasea84f82e4d06780…5270311ff5ece3
1 in β†’ 1 out8.9200 XPM109 B
AWZKhFPV…B2AaxTqs
88032dbd6f356d…4bc5e0ecd033dd
6 in β†’ 2 out15.6767 XPM967 B
AaNc3ukv…1zoav64YAJDt21Sa…kcwQByuh
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.

2.334 Γ— 10⁹⁴(95-digit number)
23342960058734078496…67208311403668017441
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
2.334 Γ— 10⁹⁴(95-digit number)
23342960058734078496…67208311403668017441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.668 Γ— 10⁹⁴(95-digit number)
46685920117468156992…34416622807336034881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
9.337 Γ— 10⁹⁴(95-digit number)
93371840234936313985…68833245614672069761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.867 Γ— 10⁹⁡(96-digit number)
18674368046987262797…37666491229344139521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.734 Γ— 10⁹⁡(96-digit number)
37348736093974525594…75332982458688279041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
7.469 Γ— 10⁹⁡(96-digit number)
74697472187949051188…50665964917376558081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.493 Γ— 10⁹⁢(97-digit number)
14939494437589810237…01331929834753116161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.987 Γ— 10⁹⁢(97-digit number)
29878988875179620475…02663859669506232321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.975 Γ— 10⁹⁢(97-digit number)
59757977750359240950…05327719339012464641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.195 Γ— 10⁹⁷(98-digit number)
11951595550071848190…10655438678024929281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.390 Γ— 10⁹⁷(98-digit number)
23903191100143696380…21310877356049858561
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,720,741 XPMΒ·at block #6,809,582 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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