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Block #790,872

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 10/31/2014, 3:31:41 PM Β· Difficulty 10.9733 Β· 6,035,932 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
70cdaa9b8cba77c5856896b2287828ae9a03e4d4e12777697c2dce77f045c43c
View on Chainz β†—

Height

#790,872

Difficulty

10.973291

Transactions

1

Size

207 B

Version

2

Bits

0af9299f

Nonce

1,547,575,395

Timestamp

10/31/2014, 3:31:41 PM

Confirmations

6,035,932

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

abd0230f007126e8c7f0c5eea7e859f73d880d08e8c352bd562eb4288074c3b3
Transactions (1)
Coinbaseabd0230f007126…2eb4288074c3b3
1 in β†’ 1 out8.2900 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.673 Γ— 10⁹⁷(98-digit number)
26730805847356667118…19634800091510540799
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
2.673 Γ— 10⁹⁷(98-digit number)
26730805847356667118…19634800091510540799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.346 Γ— 10⁹⁷(98-digit number)
53461611694713334236…39269600183021081599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.069 Γ— 10⁹⁸(99-digit number)
10692322338942666847…78539200366042163199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.138 Γ— 10⁹⁸(99-digit number)
21384644677885333694…57078400732084326399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.276 Γ— 10⁹⁸(99-digit number)
42769289355770667389…14156801464168652799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.553 Γ— 10⁹⁸(99-digit number)
85538578711541334778…28313602928337305599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.710 Γ— 10⁹⁹(100-digit number)
17107715742308266955…56627205856674611199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.421 Γ— 10⁹⁹(100-digit number)
34215431484616533911…13254411713349222399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.843 Γ— 10⁹⁹(100-digit number)
68430862969233067822…26508823426698444799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.368 Γ— 10¹⁰⁰(101-digit number)
13686172593846613564…53017646853396889599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.737 Γ— 10¹⁰⁰(101-digit number)
27372345187693227129…06035293706793779199
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:57,858,596 XPMΒ·at block #6,826,803 Β· updates every 60s
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