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Block #2,294,880

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2017, 4:15:08 PM Β· Difficulty 10.9525 Β· 4,517,472 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f88bbf764c8fd46566a6174530a8e5df688f4acf31dbf768f318082e266729ba
View on Chainz β†—

Height

#2,294,880

Difficulty

10.952532

Transactions

2

Size

540 B

Version

2

Bits

0af3d92a

Nonce

2,032,250,773

Timestamp

9/13/2017, 4:15:08 PM

Confirmations

4,517,472

Mined by

⛏️ P2SHAT3o4fhKMav3xGL9hpJH52JxoGkBDh6n9H

Merkle Root

17227f6d7dd60b8ac3d57ed16a41df194f9bc554e78a0e38af02a8aa5abbe472
Transactions (2)
Coinbase9dfde126de8592…76b7e324b9f7bb
1 in β†’ 1 out8.3300 XPM110 B
AT3o4fhK…kBDh6n9H
99e1637bdae67a…df84cd6f9e822c
2 in β†’ 1 out1199.9900 XPM340 B
AcxhUhX6…N8N8w2tm
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.

6.556 Γ— 10⁹³(94-digit number)
65560063317734034894…72613321753843607029
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
6.556 Γ— 10⁹³(94-digit number)
65560063317734034894…72613321753843607029
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.311 Γ— 10⁹⁴(95-digit number)
13112012663546806978…45226643507687214059
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.622 Γ— 10⁹⁴(95-digit number)
26224025327093613957…90453287015374428119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.244 Γ— 10⁹⁴(95-digit number)
52448050654187227915…80906574030748856239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.048 Γ— 10⁹⁡(96-digit number)
10489610130837445583…61813148061497712479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.097 Γ— 10⁹⁡(96-digit number)
20979220261674891166…23626296122995424959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.195 Γ— 10⁹⁡(96-digit number)
41958440523349782332…47252592245990849919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.391 Γ— 10⁹⁡(96-digit number)
83916881046699564665…94505184491981699839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.678 Γ— 10⁹⁢(97-digit number)
16783376209339912933…89010368983963399679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.356 Γ— 10⁹⁢(97-digit number)
33566752418679825866…78020737967926799359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.713 Γ— 10⁹⁢(97-digit number)
67133504837359651732…56041475935853598719
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:57,742,837 XPMΒ·at block #6,812,351 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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