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Block #2,833,017

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 11:21:25 AM Β· Difficulty 11.7146 Β· 4,010,483 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2c0ce43641e974247d6643d68df4404a1113ac208f71b745ad8bc8ef345e2865
View on Chainz β†—

Height

#2,833,017

Difficulty

11.714593

Transactions

1

Size

200 B

Version

2

Bits

0bb6ef8a

Nonce

181,320,331

Timestamp

9/10/2018, 11:21:25 AM

Confirmations

4,010,483

Mined by

⛏️ P2SHAU4vb4yASP18k11Gjc58cqWGoYcqkEQJAM

Merkle Root

0005eabf75b96c9b10bb7d26648988274d647c56837b1ccc76cea587346f1b6a
Transactions (1)
Coinbase0005eabf75b96c…cea587346f1b6a
1 in β†’ 1 out7.2700 XPM110 B
AU4vb4yA…cqkEQJAM
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.

2.576 Γ— 10⁹⁴(95-digit number)
25760576566624434218…76959729594165951359
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
2.576 Γ— 10⁹⁴(95-digit number)
25760576566624434218…76959729594165951359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.152 Γ— 10⁹⁴(95-digit number)
51521153133248868437…53919459188331902719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.030 Γ— 10⁹⁡(96-digit number)
10304230626649773687…07838918376663805439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.060 Γ— 10⁹⁡(96-digit number)
20608461253299547374…15677836753327610879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.121 Γ— 10⁹⁡(96-digit number)
41216922506599094749…31355673506655221759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.243 Γ— 10⁹⁡(96-digit number)
82433845013198189499…62711347013310443519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.648 Γ— 10⁹⁢(97-digit number)
16486769002639637899…25422694026620887039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.297 Γ— 10⁹⁢(97-digit number)
32973538005279275799…50845388053241774079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.594 Γ— 10⁹⁢(97-digit number)
65947076010558551599…01690776106483548159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.318 Γ— 10⁹⁷(98-digit number)
13189415202111710319…03381552212967096319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.637 Γ— 10⁹⁷(98-digit number)
26378830404223420639…06763104425934192639
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:57,992,373 XPMΒ·at block #6,843,499 Β· updates every 60s
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