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Block #434,566

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/8/2014, 8:53:22 AM Β· Difficulty 10.3487 Β· 6,375,407 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a0f9da2a209653b23c65f3904b37e6e5bfa2dae7266765f873ae97f6ce595c68
View on Chainz β†—

Height

#434,566

Difficulty

10.348658

Transactions

2

Size

873 B

Version

2

Bits

0a5941a0

Nonce

12,544

Timestamp

3/8/2014, 8:53:22 AM

Confirmations

6,375,407

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

03f257caa6724d2ac49704d141d41200105578663014f6c2639c541abd3fc79d
Transactions (2)
Coinbase31c11209163c81…f2da159050d056
1 in β†’ 1 out9.3300 XPM110 B
AeKNrjNj…1NEq95Ta
bb306332802c6f…6b6945c8d8c9c0
4 in β†’ 2 out0.9453 XPM672 B
AK9Z2jc5…X9YWxP7SANA654SS…XXR89mDn
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.

7.527 Γ— 10⁹⁡(96-digit number)
75276391435939737889…50411531077880847361
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
7.527 Γ— 10⁹⁡(96-digit number)
75276391435939737889…50411531077880847361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.505 Γ— 10⁹⁢(97-digit number)
15055278287187947577…00823062155761694721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.011 Γ— 10⁹⁢(97-digit number)
30110556574375895155…01646124311523389441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.022 Γ— 10⁹⁢(97-digit number)
60221113148751790311…03292248623046778881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.204 Γ— 10⁹⁷(98-digit number)
12044222629750358062…06584497246093557761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.408 Γ— 10⁹⁷(98-digit number)
24088445259500716124…13168994492187115521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.817 Γ— 10⁹⁷(98-digit number)
48176890519001432249…26337988984374231041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.635 Γ— 10⁹⁷(98-digit number)
96353781038002864498…52675977968748462081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.927 Γ— 10⁹⁸(99-digit number)
19270756207600572899…05351955937496924161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.854 Γ— 10⁹⁸(99-digit number)
38541512415201145799…10703911874993848321
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:57,723,858 XPMΒ·at block #6,809,972 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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