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Block #2,575,324

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/20/2018, 5:38:26 AM Β· Difficulty 10.9955 Β· 4,268,079 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
86119f67221491697d027893c2f5b4b95ca4e38b19e3e556e8ab07c1aa5f3395
View on Chainz β†—

Height

#2,575,324

Difficulty

10.995480

Transactions

1

Size

200 B

Version

2

Bits

0afed7c9

Nonce

54,430,486

Timestamp

3/20/2018, 5:38:26 AM

Confirmations

4,268,079

Mined by

⛏️ P2SHATpdx1asLLHcT9pZMpdo1VAcYPgfUPWHQE

Merkle Root

811a1df1ec077690a857ba6c0787bab055324841e71403286c3de6a466d4e3cf
Transactions (1)
Coinbase811a1df1ec0776…3de6a466d4e3cf
1 in β†’ 1 out8.2600 XPM110 B
ATpdx1as…gfUPWHQE
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.

1.021 Γ— 10⁹⁡(96-digit number)
10215788240903648392…74689129180742309119
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
1.021 Γ— 10⁹⁡(96-digit number)
10215788240903648392…74689129180742309119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.043 Γ— 10⁹⁡(96-digit number)
20431576481807296784…49378258361484618239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.086 Γ— 10⁹⁡(96-digit number)
40863152963614593569…98756516722969236479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.172 Γ— 10⁹⁡(96-digit number)
81726305927229187139…97513033445938472959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.634 Γ— 10⁹⁢(97-digit number)
16345261185445837427…95026066891876945919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.269 Γ— 10⁹⁢(97-digit number)
32690522370891674855…90052133783753891839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.538 Γ— 10⁹⁢(97-digit number)
65381044741783349711…80104267567507783679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.307 Γ— 10⁹⁷(98-digit number)
13076208948356669942…60208535135015567359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.615 Γ— 10⁹⁷(98-digit number)
26152417896713339884…20417070270031134719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.230 Γ— 10⁹⁷(98-digit number)
52304835793426679768…40834140540062269439
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:57,991,589 XPMΒ·at block #6,843,402 Β· updates every 60s
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