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Block #931,782

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/11/2015, 11:25:19 AM Β· Difficulty 10.9027 Β· 5,893,533 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d6c8c22e97ed14edea75c4890fb476e970d62d5671a2c0be2a0ee2b94aa2f71c
View on Chainz β†—

Height

#931,782

Difficulty

10.902693

Transactions

2

Size

15.86 KB

Version

2

Bits

0ae716e7

Nonce

43,079,409

Timestamp

2/11/2015, 11:25:19 AM

Confirmations

5,893,533

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

5ec57a24b73b4435eef670e1e011984254711f6b777778e4f9bdc13bc37827ee
Transactions (2)
Coinbasedbb5cf7b2d9376…0b595f1181a6ed
1 in β†’ 1 out8.5716 XPM116 B
ANSXnLY2…Sd25TjkD
703abb2bdec259…de2d70d63759af
108 in β†’ 1 out147.4000 XPM15.66 KB
AH25Uswa…TTv9GKTF
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.

8.839 Γ— 10⁹⁢(97-digit number)
88397310826557974255…85262833570165407999
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
8.839 Γ— 10⁹⁢(97-digit number)
88397310826557974255…85262833570165407999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.767 Γ— 10⁹⁷(98-digit number)
17679462165311594851…70525667140330815999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.535 Γ— 10⁹⁷(98-digit number)
35358924330623189702…41051334280661631999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.071 Γ— 10⁹⁷(98-digit number)
70717848661246379404…82102668561323263999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.414 Γ— 10⁹⁸(99-digit number)
14143569732249275880…64205337122646527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.828 Γ— 10⁹⁸(99-digit number)
28287139464498551761…28410674245293055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.657 Γ— 10⁹⁸(99-digit number)
56574278928997103523…56821348490586111999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.131 Γ— 10⁹⁹(100-digit number)
11314855785799420704…13642696981172223999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.262 Γ— 10⁹⁹(100-digit number)
22629711571598841409…27285393962344447999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.525 Γ— 10⁹⁹(100-digit number)
45259423143197682818…54570787924688895999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.051 Γ— 10⁹⁹(100-digit number)
90518846286395365637…09141575849377791999
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:57,846,624 XPMΒ·at block #6,825,314 Β· updates every 60s
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