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Block #2,838,111

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/13/2018, 11:22:15 PM Β· Difficulty 11.7178 Β· 4,006,645 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
01d9b495d7234ec39e1d7fce8aede32c254483bb7cce2f49b6e24cbd27a7a90c
View on Chainz β†—

Height

#2,838,111

Difficulty

11.717788

Transactions

1

Size

200 B

Version

2

Bits

0bb7c0f7

Nonce

398,293,593

Timestamp

9/13/2018, 11:22:15 PM

Confirmations

4,006,645

Mined by

⛏️ P2SHAZnjsMB8v3MipHeaZnC7afzAuJe7drWQRR

Merkle Root

27a015cf1ceedffb074fb0175b5267da0f9f53937cac1c5874c90ff5fefc4a3c
Transactions (1)
Coinbase27a015cf1ceedf…c90ff5fefc4a3c
1 in β†’ 1 out7.2700 XPM110 B
AZnjsMB8…e7drWQRR
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.

7.467 Γ— 10⁹⁴(95-digit number)
74670717857902314036…24300150653305959839
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
7.467 Γ— 10⁹⁴(95-digit number)
74670717857902314036…24300150653305959839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.493 Γ— 10⁹⁡(96-digit number)
14934143571580462807…48600301306611919679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.986 Γ— 10⁹⁡(96-digit number)
29868287143160925614…97200602613223839359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.973 Γ— 10⁹⁡(96-digit number)
59736574286321851229…94401205226447678719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.194 Γ— 10⁹⁢(97-digit number)
11947314857264370245…88802410452895357439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.389 Γ— 10⁹⁢(97-digit number)
23894629714528740491…77604820905790714879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.778 Γ— 10⁹⁢(97-digit number)
47789259429057480983…55209641811581429759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
9.557 Γ— 10⁹⁢(97-digit number)
95578518858114961966…10419283623162859519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.911 Γ— 10⁹⁷(98-digit number)
19115703771622992393…20838567246325719039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.823 Γ— 10⁹⁷(98-digit number)
38231407543245984786…41677134492651438079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.646 Γ— 10⁹⁷(98-digit number)
76462815086491969573…83354268985302876159
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:58,002,463 XPMΒ·at block #6,844,755 Β· updates every 60s
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