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Block #119,884

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/16/2013, 6:30:45 PM Β· Difficulty 9.7516 Β· 6,705,808 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ca9fa1a3c27ce3c9cfc33f673ce7a83b164ddae7a2f2ccdf1abc7d1a9246996e
View on Chainz β†—

Height

#119,884

Difficulty

9.751638

Transactions

1

Size

200 B

Version

2

Bits

09c06b5e

Nonce

123,649

Timestamp

8/16/2013, 6:30:45 PM

Confirmations

6,705,808

Mined by

⛏️ P2SHAGXS5BR4JtM3bWKHEDBi3oNEr4WtNUVc3H

Merkle Root

a99c4134588a5e04fa67b8869a31a0b999acb0d5cc04444a18c6479ff701fbc3
Transactions (1)
Coinbasea99c4134588a5e…c6479ff701fbc3
1 in β†’ 1 out10.5000 XPM109 B
AGXS5BR4…WtNUVc3H
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.

1.483 Γ— 10⁹⁸(99-digit number)
14833992976010685509…67062902939183885839
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
1.483 Γ— 10⁹⁸(99-digit number)
14833992976010685509…67062902939183885839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.966 Γ— 10⁹⁸(99-digit number)
29667985952021371018…34125805878367771679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.933 Γ— 10⁹⁸(99-digit number)
59335971904042742036…68251611756735543359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.186 Γ— 10⁹⁹(100-digit number)
11867194380808548407…36503223513471086719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.373 Γ— 10⁹⁹(100-digit number)
23734388761617096814…73006447026942173439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.746 Γ— 10⁹⁹(100-digit number)
47468777523234193629…46012894053884346879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.493 Γ— 10⁹⁹(100-digit number)
94937555046468387258…92025788107768693759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.898 Γ— 10¹⁰⁰(101-digit number)
18987511009293677451…84051576215537387519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.797 Γ— 10¹⁰⁰(101-digit number)
37975022018587354903…68103152431074775039
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,849,647 XPMΒ·at block #6,825,691 Β· updates every 60s
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