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Block #1,365,349

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/11/2015, 1:21:37 PM Β· Difficulty 10.8456 Β· 5,442,255 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4e93d838974840a7d21140df2ab8d8e353f9b08e98bf72c8db7e4c8274a4b026
View on Chainz β†—

Height

#1,365,349

Difficulty

10.845588

Transactions

2

Size

573 B

Version

2

Bits

0ad87872

Nonce

684,634,333

Timestamp

12/11/2015, 1:21:37 PM

Confirmations

5,442,255

Mined by

⛏️ P2SHAd6BrgMUwcSCGLqWFMBRLGs5yka98g5sCA

Merkle Root

f373c70f3c5b0d233951379b17e2ec364c2ae47736df29569eb9180ad2f14f07
Transactions (2)
Coinbasee7ffb1457a7b38…aa148f458acae7
1 in β†’ 1 out8.5200 XPM110 B
Ad6BrgMU…a98g5sCA
4d79bfa9587d91…982262f66ca886
2 in β†’ 2 out2.9887 XPM373 B
AXjH5J3t…RGMYabBxAb8Fp7GH…hxA7DGwE
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.

6.052 Γ— 10⁹⁴(95-digit number)
60525320876729795300…35989315043769299599
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
6.052 Γ— 10⁹⁴(95-digit number)
60525320876729795300…35989315043769299599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.210 Γ— 10⁹⁡(96-digit number)
12105064175345959060…71978630087538599199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.421 Γ— 10⁹⁡(96-digit number)
24210128350691918120…43957260175077198399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.842 Γ— 10⁹⁡(96-digit number)
48420256701383836240…87914520350154396799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.684 Γ— 10⁹⁡(96-digit number)
96840513402767672480…75829040700308793599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.936 Γ— 10⁹⁢(97-digit number)
19368102680553534496…51658081400617587199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.873 Γ— 10⁹⁢(97-digit number)
38736205361107068992…03316162801235174399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.747 Γ— 10⁹⁢(97-digit number)
77472410722214137984…06632325602470348799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.549 Γ— 10⁹⁷(98-digit number)
15494482144442827596…13264651204940697599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.098 Γ— 10⁹⁷(98-digit number)
30988964288885655193…26529302409881395199
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:57,704,861 XPMΒ·at block #6,807,603 Β· updates every 60s
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