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Block #2,455,814

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/3/2018, 2:31:35 PM Β· Difficulty 10.9530 Β· 4,385,019 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
85ceb67559872bbacd6f7028298d80ae932b8c283483354bc70501d3277283b6
View on Chainz β†—

Height

#2,455,814

Difficulty

10.952979

Transactions

2

Size

2.00 KB

Version

2

Bits

0af3f667

Nonce

757,700,306

Timestamp

1/3/2018, 2:31:35 PM

Confirmations

4,385,019

Mined by

⛏️ P2SHAVADWeAFGoTQ9cNqZpZptxhsQx748CSF7s

Merkle Root

b89f8ef577726397078e13a50f09e36c4a8d6eb2ac7fb46dd42efa4fc98f8ec7
Transactions (2)
Coinbase091fde220ca98e…0feba469e43ed8
1 in β†’ 1 out8.3400 XPM110 B
AVADWeAF…748CSF7s
46f4e7e61deee7…2e4fa5f439a89b
12 in β†’ 2 out139.5205 XPM1.81 KB
ALZy24uE…7X8F1gwPAPn7THxC…vxMJys8b
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.

8.791 Γ— 10⁹³(94-digit number)
87914328992866588145…75101083036543324359
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
8.791 Γ— 10⁹³(94-digit number)
87914328992866588145…75101083036543324359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.758 Γ— 10⁹⁴(95-digit number)
17582865798573317629…50202166073086648719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.516 Γ— 10⁹⁴(95-digit number)
35165731597146635258…00404332146173297439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.033 Γ— 10⁹⁴(95-digit number)
70331463194293270516…00808664292346594879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.406 Γ— 10⁹⁡(96-digit number)
14066292638858654103…01617328584693189759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.813 Γ— 10⁹⁡(96-digit number)
28132585277717308206…03234657169386379519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.626 Γ— 10⁹⁡(96-digit number)
56265170555434616413…06469314338772759039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.125 Γ— 10⁹⁢(97-digit number)
11253034111086923282…12938628677545518079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.250 Γ— 10⁹⁢(97-digit number)
22506068222173846565…25877257355091036159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.501 Γ— 10⁹⁢(97-digit number)
45012136444347693130…51754514710182072319
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:57,971,010 XPMΒ·at block #6,840,832 Β· updates every 60s
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