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Block #2,202,619

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/11/2017, 4:06:45 PM Β· Difficulty 10.9489 Β· 4,640,087 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0aa10cc7add4e05601e864cd7f78ca3a46adab3cd560ef42e30116a9243bdde9
View on Chainz β†—

Height

#2,202,619

Difficulty

10.948870

Transactions

1

Size

201 B

Version

2

Bits

0af2e926

Nonce

1,325,296,437

Timestamp

7/11/2017, 4:06:45 PM

Confirmations

4,640,087

Mined by

⛏️ P2SHAKwikV61fJXw9ugNZPYbtBmpMtMsuSUPWu

Merkle Root

7a6ef64e5b0b19bc44ba1382fae04d613237753661c704a75a8c1c744692f6bb
Transactions (1)
Coinbase7a6ef64e5b0b19…8c1c744692f6bb
1 in β†’ 1 out8.3300 XPM110 B
AKwikV61…MsuSUPWu
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.

2.578 Γ— 10⁹⁢(97-digit number)
25783483239130243709…19633611886907955199
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
2.578 Γ— 10⁹⁢(97-digit number)
25783483239130243709…19633611886907955199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.156 Γ— 10⁹⁢(97-digit number)
51566966478260487419…39267223773815910399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.031 Γ— 10⁹⁷(98-digit number)
10313393295652097483…78534447547631820799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.062 Γ— 10⁹⁷(98-digit number)
20626786591304194967…57068895095263641599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.125 Γ— 10⁹⁷(98-digit number)
41253573182608389935…14137790190527283199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.250 Γ— 10⁹⁷(98-digit number)
82507146365216779871…28275580381054566399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.650 Γ— 10⁹⁸(99-digit number)
16501429273043355974…56551160762109132799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.300 Γ— 10⁹⁸(99-digit number)
33002858546086711948…13102321524218265599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.600 Γ— 10⁹⁸(99-digit number)
66005717092173423897…26204643048436531199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.320 Γ— 10⁹⁹(100-digit number)
13201143418434684779…52409286096873062399
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:57,985,998 XPMΒ·at block #6,842,705 Β· updates every 60s
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