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Block #2,051,497

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/3/2017, 1:12:09 PM Β· Difficulty 10.7154 Β· 4,790,859 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8aa7f1e953a0ce2a12de34f8ab94d56acb83194059805188d39b8f9ce92a9a32
View on Chainz β†—

Height

#2,051,497

Difficulty

10.715352

Transactions

1

Size

199 B

Version

2

Bits

0ab7214f

Nonce

194,364,110

Timestamp

4/3/2017, 1:12:09 PM

Confirmations

4,790,859

Mined by

⛏️ P2SHAQBaRnnE38rYXUmYJiBTHk7gND7y8tvda4

Merkle Root

ad55247d8cab3bbb66f236bccadc2126db18105347aaed95a7136657f0a0ad98
Transactions (1)
Coinbasead55247d8cab3b…136657f0a0ad98
1 in β†’ 1 out8.7000 XPM109 B
AQBaRnnE…7y8tvda4
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.

3.460 Γ— 10⁹⁡(96-digit number)
34609725269513831693…80935195017277313999
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
3.460 Γ— 10⁹⁡(96-digit number)
34609725269513831693…80935195017277313999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.921 Γ— 10⁹⁡(96-digit number)
69219450539027663387…61870390034554627999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.384 Γ— 10⁹⁢(97-digit number)
13843890107805532677…23740780069109255999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.768 Γ— 10⁹⁢(97-digit number)
27687780215611065355…47481560138218511999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.537 Γ— 10⁹⁢(97-digit number)
55375560431222130710…94963120276437023999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.107 Γ— 10⁹⁷(98-digit number)
11075112086244426142…89926240552874047999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.215 Γ— 10⁹⁷(98-digit number)
22150224172488852284…79852481105748095999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.430 Γ— 10⁹⁷(98-digit number)
44300448344977704568…59704962211496191999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.860 Γ— 10⁹⁷(98-digit number)
88600896689955409136…19409924422992383999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.772 Γ— 10⁹⁸(99-digit number)
17720179337991081827…38819848845984767999
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:57,983,255 XPMΒ·at block #6,842,355 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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