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Block #902,263

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/20/2015, 5:20:55 AM Β· Difficulty 10.9403 Β· 5,894,379 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b7ae1c62825a9d77648490c04bf655d8bb7f32d59e13bacfc88102564fa55e14
View on Chainz β†—

Height

#902,263

Difficulty

10.940343

Transactions

2

Size

3.45 KB

Version

2

Bits

0af0ba4a

Nonce

35,671,271

Timestamp

1/20/2015, 5:20:55 AM

Confirmations

5,894,379

Mined by

⛏️ P2SHAY5Ni3daoxoVAWDUtptD1PhnYfdhK2irvk

Merkle Root

bf1d128fdd930d765b33853dba8cf4d9420493cf15a71cf0d36f9197d69edfd7
Transactions (2)
Coinbase2ccbb6a9bab0ef…edff3119d2167b
1 in β†’ 1 out8.3800 XPM109 B
AY5Ni3da…dhK2irvk
6403e4ad61a8f0…d592aa14525d31
22 in β†’ 2 out4989.9100 XPM3.25 KB
AZMunvRb…G9pQh9akAGkC8YQ2…5p6ZcrUA
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.

2.114 Γ— 10⁹⁡(96-digit number)
21142319455046361711…54756966295148150559
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
2.114 Γ— 10⁹⁡(96-digit number)
21142319455046361711…54756966295148150559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.228 Γ— 10⁹⁡(96-digit number)
42284638910092723423…09513932590296301119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.456 Γ— 10⁹⁡(96-digit number)
84569277820185446847…19027865180592602239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.691 Γ— 10⁹⁢(97-digit number)
16913855564037089369…38055730361185204479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.382 Γ— 10⁹⁢(97-digit number)
33827711128074178738…76111460722370408959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.765 Γ— 10⁹⁢(97-digit number)
67655422256148357477…52222921444740817919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.353 Γ— 10⁹⁷(98-digit number)
13531084451229671495…04445842889481635839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.706 Γ— 10⁹⁷(98-digit number)
27062168902459342991…08891685778963271679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.412 Γ— 10⁹⁷(98-digit number)
54124337804918685982…17783371557926543359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.082 Γ— 10⁹⁸(99-digit number)
10824867560983737196…35566743115853086719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.164 Γ— 10⁹⁸(99-digit number)
21649735121967474392…71133486231706173439
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:57,617,138 XPMΒ·at block #6,796,641 Β· updates every 60s
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