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Block #1,903,175

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/20/2016, 12:17:26 PM Β· Difficulty 10.7825 Β· 4,939,245 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f141e1d7bbf070f0c6ec43cb33d188f663a1e8caabc120177fa0836990b34607
View on Chainz β†—

Height

#1,903,175

Difficulty

10.782504

Transactions

1

Size

200 B

Version

2

Bits

0ac8522d

Nonce

117,952,672

Timestamp

12/20/2016, 12:17:26 PM

Confirmations

4,939,245

Mined by

⛏️ P2SHAJR18cz315WVFzvBjy1wrD7rzZgk7drBCU

Merkle Root

67e136bba27339a5a69bed26e857e1a74c278b7945944ff893cf9c1af32ffb86
Transactions (1)
Coinbase67e136bba27339…cf9c1af32ffb86
1 in β†’ 1 out8.5900 XPM110 B
AJR18cz3…gk7drBCU
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.

2.238 Γ— 10⁹⁴(95-digit number)
22384371078582017283…47061973902262883239
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
2.238 Γ— 10⁹⁴(95-digit number)
22384371078582017283…47061973902262883239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.476 Γ— 10⁹⁴(95-digit number)
44768742157164034566…94123947804525766479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.953 Γ— 10⁹⁴(95-digit number)
89537484314328069132…88247895609051532959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.790 Γ— 10⁹⁡(96-digit number)
17907496862865613826…76495791218103065919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.581 Γ— 10⁹⁡(96-digit number)
35814993725731227652…52991582436206131839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.162 Γ— 10⁹⁡(96-digit number)
71629987451462455305…05983164872412263679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.432 Γ— 10⁹⁢(97-digit number)
14325997490292491061…11966329744824527359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.865 Γ— 10⁹⁢(97-digit number)
28651994980584982122…23932659489649054719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.730 Γ— 10⁹⁢(97-digit number)
57303989961169964244…47865318979298109439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.146 Γ— 10⁹⁷(98-digit number)
11460797992233992848…95730637958596218879
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:57,983,774 XPMΒ·at block #6,842,419 Β· updates every 60s
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