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Block #2,812,142

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/27/2018, 11:44:44 AM Β· Difficulty 11.6689 Β· 4,021,712 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
0c5723e53b4be3a8a14f616b56fc21a278b78644983685b75b343714b5740a04
View on Chainz β†—

Height

#2,812,142

Difficulty

11.668869

Transactions

2

Size

576 B

Version

2

Bits

0bab3b08

Nonce

930,548,034

Timestamp

8/27/2018, 11:44:44 AM

Confirmations

4,021,712

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

0845d54fe5a2a2e0a8416c4058bfa8d0129665ded4cb7bd06b24c7a64a22f4a9
Transactions (2)
Coinbasea302d053ac6237…c473a887926759
1 in β†’ 1 out7.3400 XPM110 B
AZtxQr2F…7grUWrUz
dfd84d061847db…c23e2ec0c04b7a
2 in β†’ 2 out104.6087 XPM375 B
ATsX74ZL…1DwgaqFPAJyqt5pZ…v1d3dTkX
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.

3.796 Γ— 10⁹⁢(97-digit number)
37969797826514206454…71823901093062911999
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
3.796 Γ— 10⁹⁢(97-digit number)
37969797826514206454…71823901093062911999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.593 Γ— 10⁹⁢(97-digit number)
75939595653028412908…43647802186125823999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.518 Γ— 10⁹⁷(98-digit number)
15187919130605682581…87295604372251647999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.037 Γ— 10⁹⁷(98-digit number)
30375838261211365163…74591208744503295999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.075 Γ— 10⁹⁷(98-digit number)
60751676522422730326…49182417489006591999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.215 Γ— 10⁹⁸(99-digit number)
12150335304484546065…98364834978013183999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.430 Γ— 10⁹⁸(99-digit number)
24300670608969092130…96729669956026367999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.860 Γ— 10⁹⁸(99-digit number)
48601341217938184261…93459339912052735999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.720 Γ— 10⁹⁸(99-digit number)
97202682435876368522…86918679824105471999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.944 Γ— 10⁹⁹(100-digit number)
19440536487175273704…73837359648210943999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.888 Γ— 10⁹⁹(100-digit number)
38881072974350547408…47674719296421887999
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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