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Block #792,211

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 11/1/2014, 1:18:19 PM Β· Difficulty 10.9735 Β· 6,018,746 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a92b748e2defb7916a3639540dfda9b3eaebba6bb6cbb41d3d085432676a26d8
View on Chainz β†—

Height

#792,211

Difficulty

10.973513

Transactions

2

Size

720 B

Version

2

Bits

0af93821

Nonce

1,823,765,700

Timestamp

11/1/2014, 1:18:19 PM

Confirmations

6,018,746

Mined by

⛏️ P2SHAKR9cQXtqXhqGayajypTrpP6XzRBrLcGKp

Merkle Root

7560962c93fc0cdcb7b5e983de07e6427b550a7cb2b438338563250fbc915f7b
Transactions (2)
Coinbase8a35baf074ca4d…00efbfa0784e2b
1 in β†’ 1 out8.3000 XPM109 B
AKR9cQXt…RBrLcGKp
133addf13cac75…47591d1bb9359d
3 in β†’ 2 out1315.8113 XPM521 B
AY3AFkrW…vkPQYHoUAcAFW717…V1pWEX3J
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.

1.178 Γ— 10⁹⁴(95-digit number)
11780973626376531867…70686223205649726559
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
1.178 Γ— 10⁹⁴(95-digit number)
11780973626376531867…70686223205649726559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.356 Γ— 10⁹⁴(95-digit number)
23561947252753063735…41372446411299453119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.712 Γ— 10⁹⁴(95-digit number)
47123894505506127470…82744892822598906239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.424 Γ— 10⁹⁴(95-digit number)
94247789011012254940…65489785645197812479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.884 Γ— 10⁹⁡(96-digit number)
18849557802202450988…30979571290395624959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.769 Γ— 10⁹⁡(96-digit number)
37699115604404901976…61959142580791249919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.539 Γ— 10⁹⁡(96-digit number)
75398231208809803952…23918285161582499839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.507 Γ— 10⁹⁢(97-digit number)
15079646241761960790…47836570323164999679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.015 Γ— 10⁹⁢(97-digit number)
30159292483523921580…95673140646329999359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.031 Γ— 10⁹⁢(97-digit number)
60318584967047843161…91346281292659998719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.206 Γ— 10⁹⁷(98-digit number)
12063716993409568632…82692562585319997439
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:57,731,756 XPMΒ·at block #6,810,956 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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