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Block #2,829,524

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/8/2018, 1:27:39 AM Β· Difficulty 11.7133 Β· 4,012,573 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
df7327677b0f804345f1afd1412820fcd2a82937285f078c865cb8baf6ada1f3
View on Chainz β†—

Height

#2,829,524

Difficulty

11.713308

Transactions

1

Size

200 B

Version

2

Bits

0bb69b58

Nonce

616,681,031

Timestamp

9/8/2018, 1:27:39 AM

Confirmations

4,012,573

Mined by

⛏️ P2SHAUwfW8zzAsWKyisgsyivhiZD1Ufy2nJieo

Merkle Root

7c4444ac841cfb914c7f967f5889c7017f5f04d5603a489b4b71a8a996863c16
Transactions (1)
Coinbase7c4444ac841cfb…71a8a996863c16
1 in β†’ 1 out7.2800 XPM110 B
AUwfW8zz…fy2nJieo
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.

1.152 Γ— 10⁹⁡(96-digit number)
11528753959105291247…62529524950942914259
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
1.152 Γ— 10⁹⁡(96-digit number)
11528753959105291247…62529524950942914259
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.305 Γ— 10⁹⁡(96-digit number)
23057507918210582494…25059049901885828519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.611 Γ— 10⁹⁡(96-digit number)
46115015836421164988…50118099803771657039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.223 Γ— 10⁹⁡(96-digit number)
92230031672842329977…00236199607543314079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.844 Γ— 10⁹⁢(97-digit number)
18446006334568465995…00472399215086628159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.689 Γ— 10⁹⁢(97-digit number)
36892012669136931990…00944798430173256319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.378 Γ— 10⁹⁢(97-digit number)
73784025338273863981…01889596860346512639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.475 Γ— 10⁹⁷(98-digit number)
14756805067654772796…03779193720693025279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.951 Γ— 10⁹⁷(98-digit number)
29513610135309545592…07558387441386050559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.902 Γ— 10⁹⁷(98-digit number)
59027220270619091185…15116774882772101119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.180 Γ— 10⁹⁸(99-digit number)
11805444054123818237…30233549765544202239
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,981,162 XPMΒ·at block #6,842,096 Β· updates every 60s
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