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Block #1,835,656

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/5/2016, 12:46:06 AM Β· Difficulty 10.6719 Β· 5,006,618 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d52390ff2080ca3d525fa50f6169993a36626188d6f6ada4f5905d5f14c3e2ff
View on Chainz β†—

Height

#1,835,656

Difficulty

10.671871

Transactions

2

Size

539 B

Version

2

Bits

0aabffc1

Nonce

1,437,132,091

Timestamp

11/5/2016, 12:46:06 AM

Confirmations

5,006,618

Mined by

⛏️ P2SHAUwgEX9kpmcxKvfTf1NUqaJgpt3C1Ho62b

Merkle Root

df74b1b54fddc0372cc0443507f1fc8eccd537c8a06a46d015a004cdd0784b4e
Transactions (2)
Coinbase9c388df2d0c8a1…f5bb4223c25325
1 in β†’ 1 out8.7800 XPM110 B
AUwgEX9k…3C1Ho62b
73bf3098c673fe…42068daf3eff34
2 in β†’ 1 out0.2238 XPM339 B
AUKV3Goi…ajcvvDKN
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.

1.961 Γ— 10⁹⁡(96-digit number)
19610913545396091334…13757557993545582079
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
1.961 Γ— 10⁹⁡(96-digit number)
19610913545396091334…13757557993545582079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.922 Γ— 10⁹⁡(96-digit number)
39221827090792182668…27515115987091164159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.844 Γ— 10⁹⁡(96-digit number)
78443654181584365337…55030231974182328319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.568 Γ— 10⁹⁢(97-digit number)
15688730836316873067…10060463948364656639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.137 Γ— 10⁹⁢(97-digit number)
31377461672633746135…20120927896729313279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.275 Γ— 10⁹⁢(97-digit number)
62754923345267492270…40241855793458626559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.255 Γ— 10⁹⁷(98-digit number)
12550984669053498454…80483711586917253119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.510 Γ— 10⁹⁷(98-digit number)
25101969338106996908…60967423173834506239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.020 Γ— 10⁹⁷(98-digit number)
50203938676213993816…21934846347669012479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.004 Γ— 10⁹⁸(99-digit number)
10040787735242798763…43869692695338024959
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:57,982,593 XPMΒ·at block #6,842,273 Β· updates every 60s
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