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Block #243,200

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/4/2013, 4:09:15 AM Β· Difficulty 9.9611 Β· 6,565,669 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
39e05e0a0a4cc38380408db288b8894589e5edfb10f3895444131cf4fdc688fb
View on Chainz β†—

Height

#243,200

Difficulty

9.961122

Transactions

1

Size

200 B

Version

2

Bits

09f60c1d

Nonce

274,806

Timestamp

11/4/2013, 4:09:15 AM

Confirmations

6,565,669

Mined by

⛏️ P2SHAPpAmzuiarcDRTEE9yddUu8j7EbKYJJ5pB

Merkle Root

d3dba84377455e52a9b94a621bc6bad898c6e11c66ff7995f72aecf013ab313a
Transactions (1)
Coinbased3dba84377455e…2aecf013ab313a
1 in β†’ 1 out10.0600 XPM109 B
APpAmzui…bKYJJ5pB
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.

2.195 Γ— 10⁹⁷(98-digit number)
21951794019307054977…95176616701981603839
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
2.195 Γ— 10⁹⁷(98-digit number)
21951794019307054977…95176616701981603839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.390 Γ— 10⁹⁷(98-digit number)
43903588038614109954…90353233403963207679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.780 Γ— 10⁹⁷(98-digit number)
87807176077228219908…80706466807926415359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.756 Γ— 10⁹⁸(99-digit number)
17561435215445643981…61412933615852830719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.512 Γ— 10⁹⁸(99-digit number)
35122870430891287963…22825867231705661439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.024 Γ— 10⁹⁸(99-digit number)
70245740861782575926…45651734463411322879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.404 Γ— 10⁹⁹(100-digit number)
14049148172356515185…91303468926822645759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.809 Γ— 10⁹⁹(100-digit number)
28098296344713030370…82606937853645291519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.619 Γ— 10⁹⁹(100-digit number)
56196592689426060741…65213875707290583039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.123 Γ— 10¹⁰⁰(101-digit number)
11239318537885212148…30427751414581166079
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:57,715,002 XPMΒ·at block #6,808,868 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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