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Block #2,165,377

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/18/2017, 3:32:30 AM Β· Difficulty 10.8984 Β· 4,651,938 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8bca2a09333785f209ae3ce4deb9a5120077701742a296b75f258c60debdcb85
View on Chainz β†—

Height

#2,165,377

Difficulty

10.898442

Transactions

3

Size

4.04 KB

Version

2

Bits

0ae6004e

Nonce

678,873,656

Timestamp

6/18/2017, 3:32:30 AM

Confirmations

4,651,938

Mined by

⛏️ P2SHAJa9fe3haBUEzSxehzkTNpfXQ8HeZ5R6Q3

Merkle Root

993cd683e2b2f8b608fc120474df771688c3dbcf793db91d64fcb12b33261d23
Transactions (3)
Coinbase8ba9b442809f70…98133fbf3ba5d3
1 in β†’ 1 out8.4800 XPM109 B
AJa9fe3h…HeZ5R6Q3
85ade12feba78b…0aac6d628a110c
9 in β†’ 1 out2132.2615 XPM1.35 KB
AdLv38Pf…k1z3e6Dc
0e0f4b072bea24…0b645668497e01
17 in β†’ 1 out4903.3471 XPM2.50 KB
AMnF3Bvi…vraANRg7
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.

3.284 Γ— 10⁹⁢(97-digit number)
32845111160283583924…81263473888626004479
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
3.284 Γ— 10⁹⁢(97-digit number)
32845111160283583924…81263473888626004479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.569 Γ— 10⁹⁢(97-digit number)
65690222320567167849…62526947777252008959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.313 Γ— 10⁹⁷(98-digit number)
13138044464113433569…25053895554504017919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.627 Γ— 10⁹⁷(98-digit number)
26276088928226867139…50107791109008035839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.255 Γ— 10⁹⁷(98-digit number)
52552177856453734279…00215582218016071679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.051 Γ— 10⁹⁸(99-digit number)
10510435571290746855…00431164436032143359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.102 Γ— 10⁹⁸(99-digit number)
21020871142581493711…00862328872064286719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.204 Γ— 10⁹⁸(99-digit number)
42041742285162987423…01724657744128573439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.408 Γ— 10⁹⁸(99-digit number)
84083484570325974846…03449315488257146879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.681 Γ— 10⁹⁹(100-digit number)
16816696914065194969…06898630976514293759
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:57,782,565 XPMΒ·at block #6,817,314 Β· updates every 60s
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