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Block #472,361

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2014, 5:56:06 AM Β· Difficulty 10.4331 Β· 6,345,411 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6d28c55a7b28110779bdaf4592083caa16d3d1f94de55bde5d5db58d84c2ffc1
View on Chainz β†—

Height

#472,361

Difficulty

10.433116

Transactions

1

Size

200 B

Version

2

Bits

0a6ee0aa

Nonce

555,044

Timestamp

4/3/2014, 5:56:06 AM

Confirmations

6,345,411

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

19c3baf14aa7ee3e550e99572d2b1f9d58b90faaa5c0f31de99ecc74c3d6bc1d
Transactions (1)
Coinbase19c3baf14aa7ee…9ecc74c3d6bc1d
1 in β†’ 1 out9.1700 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.

1.046 Γ— 10⁹⁡(96-digit number)
10463200979619560180…77095171157830558179
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
1.046 Γ— 10⁹⁡(96-digit number)
10463200979619560180…77095171157830558179
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.092 Γ— 10⁹⁡(96-digit number)
20926401959239120360…54190342315661116359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.185 Γ— 10⁹⁡(96-digit number)
41852803918478240720…08380684631322232719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.370 Γ— 10⁹⁡(96-digit number)
83705607836956481440…16761369262644465439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.674 Γ— 10⁹⁢(97-digit number)
16741121567391296288…33522738525288930879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.348 Γ— 10⁹⁢(97-digit number)
33482243134782592576…67045477050577861759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.696 Γ— 10⁹⁢(97-digit number)
66964486269565185152…34090954101155723519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.339 Γ— 10⁹⁷(98-digit number)
13392897253913037030…68181908202311447039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.678 Γ— 10⁹⁷(98-digit number)
26785794507826074060…36363816404622894079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.357 Γ— 10⁹⁷(98-digit number)
53571589015652148121…72727632809245788159
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 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
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,786,233 XPMΒ·at block #6,817,771 Β· updates every 60s
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