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Block #410,505

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/19/2014, 3:04:18 AM Β· Difficulty 10.4280 Β· 6,416,338 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
096e9d0e5042fb7679fbee7006ab20f20bc7dd3b50847a4084262ae66695c380
View on Chainz β†—

Height

#410,505

Difficulty

10.427975

Transactions

2

Size

689 B

Version

2

Bits

0a6d8fc0

Nonce

273,588

Timestamp

2/19/2014, 3:04:18 AM

Confirmations

6,416,338

Mined by

⛏️ P2SHAWfwEdv8ypK2osv5UwMfixqSteQkSPxiE3

Merkle Root

a3ac7a7c1fe5302f3f38df2e8f37928792251488874f865af627951c01590733
Transactions (2)
Coinbaseddc11c6755b761…318f28c6495415
1 in β†’ 1 out9.1979 XPM109 B
AWfwEdv8…QkSPxiE3
ff9962c007ed5b…262ffc9a37b715
3 in β†’ 1 out6.1800 XPM489 B
Ad2hD38o…VYagYLe6
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.

4.499 Γ— 10⁹⁢(97-digit number)
44990494002514904879…77668934869784517179
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
4.499 Γ— 10⁹⁢(97-digit number)
44990494002514904879…77668934869784517179
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.998 Γ— 10⁹⁢(97-digit number)
89980988005029809759…55337869739569034359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.799 Γ— 10⁹⁷(98-digit number)
17996197601005961951…10675739479138068719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.599 Γ— 10⁹⁷(98-digit number)
35992395202011923903…21351478958276137439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.198 Γ— 10⁹⁷(98-digit number)
71984790404023847807…42702957916552274879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.439 Γ— 10⁹⁸(99-digit number)
14396958080804769561…85405915833104549759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.879 Γ— 10⁹⁸(99-digit number)
28793916161609539122…70811831666209099519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.758 Γ— 10⁹⁸(99-digit number)
57587832323219078245…41623663332418199039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.151 Γ— 10⁹⁹(100-digit number)
11517566464643815649…83247326664836398079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.303 Γ— 10⁹⁹(100-digit number)
23035132929287631298…66494653329672796159
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:57,858,909 XPMΒ·at block #6,826,842 Β· updates every 60s
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