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Block #2,477,904

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/17/2018, 10:48:31 PM Β· Difficulty 10.9652 Β· 4,365,042 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
22aacbcc856e735f48faff474db37cbe15acccf9145231f670f44f0ed9a57565
View on Chainz β†—

Height

#2,477,904

Difficulty

10.965192

Transactions

2

Size

574 B

Version

2

Bits

0af716d9

Nonce

410,623,742

Timestamp

1/17/2018, 10:48:31 PM

Confirmations

4,365,042

Mined by

⛏️ P2SHAHaKsWS2H7rx5U8GiwTtkPUsq1pig3hxYk

Merkle Root

07c5b9658197faa9d5e4b7e793f782db04019506298458dea626005f6538193a
Transactions (2)
Coinbasecfef788cfdca19…ba071084cc64af
1 in β†’ 1 out8.3100 XPM109 B
AHaKsWS2…pig3hxYk
f47291c1f5c9ee…e61b2af2170595
2 in β†’ 2 out16.9800 XPM375 B
AdbYjmJ6…BQK2Lr1bAbEXh1ds…zDjdTYYc
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.

8.497 Γ— 10⁹³(94-digit number)
84978656892927114670…42053920349799528839
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
8.497 Γ— 10⁹³(94-digit number)
84978656892927114670…42053920349799528839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.699 Γ— 10⁹⁴(95-digit number)
16995731378585422934…84107840699599057679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.399 Γ— 10⁹⁴(95-digit number)
33991462757170845868…68215681399198115359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.798 Γ— 10⁹⁴(95-digit number)
67982925514341691736…36431362798396230719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.359 Γ— 10⁹⁡(96-digit number)
13596585102868338347…72862725596792461439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.719 Γ— 10⁹⁡(96-digit number)
27193170205736676694…45725451193584922879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.438 Γ— 10⁹⁡(96-digit number)
54386340411473353389…91450902387169845759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.087 Γ— 10⁹⁢(97-digit number)
10877268082294670677…82901804774339691519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.175 Γ— 10⁹⁢(97-digit number)
21754536164589341355…65803609548679383039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.350 Γ— 10⁹⁢(97-digit number)
43509072329178682711…31607219097358766079
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:57,987,919 XPMΒ·at block #6,842,945 Β· updates every 60s
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