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Block #854,159

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/15/2014, 10:09:25 AM Β· Difficulty 10.9687 Β· 5,977,899 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
02cfc3980d02b5d9b9f7ed2534ef26705cf4375ba71c2f638531bc7bc32468c9
View on Chainz β†—

Height

#854,159

Difficulty

10.968750

Transactions

2

Size

399 B

Version

2

Bits

0af7fffe

Nonce

784,304,069

Timestamp

12/15/2014, 10:09:25 AM

Confirmations

5,977,899

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2208c961070073d0642a0eb178b6d92c4c37c2ec487591ac3c51618bba302150
Transactions (2)
Coinbase413f39c3f2c55f…fdc72120b82859
1 in β†’ 1 out8.3178 XPM116 B
ANSXnLY2…Sd25TjkD
e3c8aa43f895b0…316aeb57ff51a7
1 in β†’ 1 out0.0112 XPM193 B
AaTLVNJu…fyojGBwo
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.

3.002 Γ— 10⁹⁴(95-digit number)
30025000637448996374…12597087088813016959
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
3.002 Γ— 10⁹⁴(95-digit number)
30025000637448996374…12597087088813016959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.005 Γ— 10⁹⁴(95-digit number)
60050001274897992749…25194174177626033919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.201 Γ— 10⁹⁡(96-digit number)
12010000254979598549…50388348355252067839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.402 Γ— 10⁹⁡(96-digit number)
24020000509959197099…00776696710504135679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.804 Γ— 10⁹⁡(96-digit number)
48040001019918394199…01553393421008271359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.608 Γ— 10⁹⁡(96-digit number)
96080002039836788398…03106786842016542719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.921 Γ— 10⁹⁢(97-digit number)
19216000407967357679…06213573684033085439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.843 Γ— 10⁹⁢(97-digit number)
38432000815934715359…12427147368066170879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.686 Γ— 10⁹⁢(97-digit number)
76864001631869430718…24854294736132341759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.537 Γ— 10⁹⁷(98-digit number)
15372800326373886143…49708589472264683519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.074 Γ— 10⁹⁷(98-digit number)
30745600652747772287…99417178944529367039
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
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