XPM Prime Explorer symbol
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Block #579,027

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/6/2014, 1:10:42 PM Β· Difficulty 10.9676 Β· 6,229,994 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
650d4b770775e36e18f0e7ced5100634bdff7bbe952d9392a188a3b3de74e939
View on Chainz β†—

Height

#579,027

Difficulty

10.967556

Transactions

2

Size

97.66 KB

Version

2

Bits

0af7b1c0

Nonce

190,879,844

Timestamp

6/6/2014, 1:10:42 PM

Confirmations

6,229,994

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2c45ddbb3313a82aee5b5e4c98acedab85377f3b58f5a9a6290e94f4fcbe934f
Transactions (2)
Coinbase575e47938c7222…b5b5a2272af208
1 in β†’ 1 out9.3000 XPM116 B
ANSXnLY2…Sd25TjkD
7dcadc3aefae4d…13eda0684a418e
674 in β†’ 2 out235.0100 XPM97.46 KB
AdpfTa6J…5knLdNjAAchmN8LE…XpHijvds
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.

1.161 Γ— 10⁹⁷(98-digit number)
11613986935642883620…75322717218282461019
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
1.161 Γ— 10⁹⁷(98-digit number)
11613986935642883620…75322717218282461019
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.322 Γ— 10⁹⁷(98-digit number)
23227973871285767241…50645434436564922039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.645 Γ— 10⁹⁷(98-digit number)
46455947742571534483…01290868873129844079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.291 Γ— 10⁹⁷(98-digit number)
92911895485143068967…02581737746259688159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.858 Γ— 10⁹⁸(99-digit number)
18582379097028613793…05163475492519376319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.716 Γ— 10⁹⁸(99-digit number)
37164758194057227586…10326950985038752639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.432 Γ— 10⁹⁸(99-digit number)
74329516388114455173…20653901970077505279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.486 Γ— 10⁹⁹(100-digit number)
14865903277622891034…41307803940155010559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.973 Γ— 10⁹⁹(100-digit number)
29731806555245782069…82615607880310021119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.946 Γ— 10⁹⁹(100-digit number)
59463613110491564139…65231215760620042239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.189 Γ— 10¹⁰⁰(101-digit number)
11892722622098312827…30462431521240084479
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,716,230 XPMΒ·at block #6,809,020 Β· updates every 60s
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