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Block #2,782,823

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/7/2018, 5:20:44 AM Β· Difficulty 11.6588 Β· 4,050,716 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3318e83bff872e65119397887e1223b1b2ce7bb06a4b2fbec53e4a9389a964c2
View on Chainz β†—

Height

#2,782,823

Difficulty

11.658754

Transactions

2

Size

722 B

Version

2

Bits

0ba8a41b

Nonce

1,552,825,904

Timestamp

8/7/2018, 5:20:44 AM

Confirmations

4,050,716

Mined by

⛏️ P2SHAcGPG19capZLn3AHTXdkiRRJRApzKigFQ7

Merkle Root

b7e788394883719ef6054b3e6a7e2303ea0d47930db7cda69838f88c92dbc2af
Transactions (2)
Coinbased228c482189b24…29a30b0ddaed13
1 in β†’ 1 out7.3500 XPM109 B
AcGPG19c…pzKigFQ7
41efa62050b03d…4a3d1c6aa5ba37
3 in β†’ 2 out200.0110 XPM523 B
AejmSw8c…t8FLBKoDAJhMnsij…c6YMRfPF
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.

1.521 Γ— 10⁹⁴(95-digit number)
15217907759978650309…04711249133438048279
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
1.521 Γ— 10⁹⁴(95-digit number)
15217907759978650309…04711249133438048279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.043 Γ— 10⁹⁴(95-digit number)
30435815519957300619…09422498266876096559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.087 Γ— 10⁹⁴(95-digit number)
60871631039914601239…18844996533752193119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.217 Γ— 10⁹⁡(96-digit number)
12174326207982920247…37689993067504386239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.434 Γ— 10⁹⁡(96-digit number)
24348652415965840495…75379986135008772479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.869 Γ— 10⁹⁡(96-digit number)
48697304831931680991…50759972270017544959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.739 Γ— 10⁹⁡(96-digit number)
97394609663863361982…01519944540035089919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.947 Γ— 10⁹⁢(97-digit number)
19478921932772672396…03039889080070179839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.895 Γ— 10⁹⁢(97-digit number)
38957843865545344792…06079778160140359679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.791 Γ— 10⁹⁢(97-digit number)
77915687731090689585…12159556320280719359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.558 Γ— 10⁹⁷(98-digit number)
15583137546218137917…24319112640561438719
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:57,912,511 XPMΒ·at block #6,833,538 Β· updates every 60s
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