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Block #354,646

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/11/2014, 4:09:15 PM Β· Difficulty 10.3478 Β· 6,453,206 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ff209aaf38cc26c67152d23745294045da97889b2f15bb7729e7c802522d8b5a
View on Chainz β†—

Height

#354,646

Difficulty

10.347810

Transactions

1

Size

204 B

Version

2

Bits

0a590a19

Nonce

47,513

Timestamp

1/11/2014, 4:09:15 PM

Confirmations

6,453,206

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

8bae421516cf179a90c216751d967e8dd9ab663691f915a36d7bbaa64d93994b
Transactions (1)
Coinbase8bae421516cf17…7bbaa64d93994b
1 in β†’ 1 out9.3200 XPM116 B
AbwWkWZt…kawDhufa
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.

1.908 Γ— 10⁹⁰(91-digit number)
19087058772406339732…37018871626336399739
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
1.908 Γ— 10⁹⁰(91-digit number)
19087058772406339732…37018871626336399739
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.817 Γ— 10⁹⁰(91-digit number)
38174117544812679465…74037743252672799479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.634 Γ— 10⁹⁰(91-digit number)
76348235089625358930…48075486505345598959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.526 Γ— 10⁹¹(92-digit number)
15269647017925071786…96150973010691197919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.053 Γ— 10⁹¹(92-digit number)
30539294035850143572…92301946021382395839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.107 Γ— 10⁹¹(92-digit number)
61078588071700287144…84603892042764791679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.221 Γ— 10⁹²(93-digit number)
12215717614340057428…69207784085529583359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.443 Γ— 10⁹²(93-digit number)
24431435228680114857…38415568171059166719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.886 Γ— 10⁹²(93-digit number)
48862870457360229715…76831136342118333439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.772 Γ— 10⁹²(93-digit number)
97725740914720459430…53662272684236666879
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:57,706,856 XPMΒ·at block #6,807,851 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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