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Block #1,106,090

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/15/2015, 7:16:06 AM Β· Difficulty 10.7924 Β· 5,708,944 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5f7362f2b86d85c81a1afa3fc287f8dd7343ca005a24c590af8fcc8f6db2288b
View on Chainz β†—

Height

#1,106,090

Difficulty

10.792425

Transactions

1

Size

200 B

Version

2

Bits

0acadc5f

Nonce

273,212,640

Timestamp

6/15/2015, 7:16:06 AM

Confirmations

5,708,944

Mined by

⛏️ P2SHAJvH5NPpuZubcq2gAywXNPHC7JNkB5B3fF

Merkle Root

87bb4a8e50ef028699eaeada5fe47cc889c09678a41e282e502bc55af10258fd
Transactions (1)
Coinbase87bb4a8e50ef02…2bc55af10258fd
1 in β†’ 1 out8.5700 XPM110 B
AJvH5NPp…NkB5B3fF
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.

4.287 Γ— 10⁹⁡(96-digit number)
42874831738140964357…03527316640820984319
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
4.287 Γ— 10⁹⁡(96-digit number)
42874831738140964357…03527316640820984319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.574 Γ— 10⁹⁡(96-digit number)
85749663476281928715…07054633281641968639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.714 Γ— 10⁹⁢(97-digit number)
17149932695256385743…14109266563283937279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.429 Γ— 10⁹⁢(97-digit number)
34299865390512771486…28218533126567874559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.859 Γ— 10⁹⁢(97-digit number)
68599730781025542972…56437066253135749119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.371 Γ— 10⁹⁷(98-digit number)
13719946156205108594…12874132506271498239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.743 Γ— 10⁹⁷(98-digit number)
27439892312410217188…25748265012542996479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.487 Γ— 10⁹⁷(98-digit number)
54879784624820434377…51496530025085992959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.097 Γ— 10⁹⁸(99-digit number)
10975956924964086875…02993060050171985919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.195 Γ— 10⁹⁸(99-digit number)
21951913849928173751…05986120100343971839
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:57,764,362 XPMΒ·at block #6,815,033 Β· updates every 60s
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