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Block #470,688

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/2/2014, 2:27:13 AM Β· Difficulty 10.4296 Β· 6,345,935 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b36dcaad3929f57adf4988da69747c5763ceaed545b9938631994695977f4a5e
View on Chainz β†—

Height

#470,688

Difficulty

10.429606

Transactions

1

Size

204 B

Version

2

Bits

0a6dfaaa

Nonce

48,185

Timestamp

4/2/2014, 2:27:13 AM

Confirmations

6,345,935

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

afc3df871b135705d39af351c1b15eef4269ff9b27c7554567d077484e759ba7
Transactions (1)
Coinbaseafc3df871b1357…d077484e759ba7
1 in β†’ 1 out9.1800 XPM110 B
AeKNrjNj…1NEq95Ta
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.

8.470 Γ— 10¹⁰³(104-digit number)
84700362766307476974…30293546013896026881
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
8.470 Γ— 10¹⁰³(104-digit number)
84700362766307476974…30293546013896026881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.694 Γ— 10¹⁰⁴(105-digit number)
16940072553261495394…60587092027792053761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.388 Γ— 10¹⁰⁴(105-digit number)
33880145106522990789…21174184055584107521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.776 Γ— 10¹⁰⁴(105-digit number)
67760290213045981579…42348368111168215041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.355 Γ— 10¹⁰⁡(106-digit number)
13552058042609196315…84696736222336430081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.710 Γ— 10¹⁰⁡(106-digit number)
27104116085218392631…69393472444672860161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.420 Γ— 10¹⁰⁡(106-digit number)
54208232170436785263…38786944889345720321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.084 Γ— 10¹⁰⁢(107-digit number)
10841646434087357052…77573889778691440641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.168 Γ— 10¹⁰⁢(107-digit number)
21683292868174714105…55147779557382881281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.336 Γ— 10¹⁰⁢(107-digit number)
43366585736349428211…10295559114765762561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,777,107 XPMΒ·at block #6,816,622 Β· updates every 60s
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