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Block #2,844,811

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/18/2018, 12:01:42 PM Β· Difficulty 11.7279 Β· 3,999,150 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
57df0eb201953f9412d97d46e0c8261424b9186230c9910ba85ecfa63268f752
View on Chainz β†—

Height

#2,844,811

Difficulty

11.727897

Transactions

1

Size

201 B

Version

2

Bits

0bba5779

Nonce

46,714,005

Timestamp

9/18/2018, 12:01:42 PM

Confirmations

3,999,150

Mined by

⛏️ P2SHAdKFfbMyrUzKAy4SpfE2djpSfaJew2UGXe

Merkle Root

4303a93a677d7dac8404540f4cd0eef32e5b22d17fa37a6afdd8278fab356671
Transactions (1)
Coinbase4303a93a677d7d…d8278fab356671
1 in β†’ 1 out7.2600 XPM110 B
AdKFfbMy…Jew2UGXe
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.

1.299 Γ— 10⁹⁸(99-digit number)
12999426251474004181…88842341017246699519
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
1.299 Γ— 10⁹⁸(99-digit number)
12999426251474004181…88842341017246699519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.599 Γ— 10⁹⁸(99-digit number)
25998852502948008362…77684682034493399039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.199 Γ— 10⁹⁸(99-digit number)
51997705005896016725…55369364068986798079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.039 Γ— 10⁹⁹(100-digit number)
10399541001179203345…10738728137973596159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.079 Γ— 10⁹⁹(100-digit number)
20799082002358406690…21477456275947192319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.159 Γ— 10⁹⁹(100-digit number)
41598164004716813380…42954912551894384639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.319 Γ— 10⁹⁹(100-digit number)
83196328009433626760…85909825103788769279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.663 Γ— 10¹⁰⁰(101-digit number)
16639265601886725352…71819650207577538559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.327 Γ— 10¹⁰⁰(101-digit number)
33278531203773450704…43639300415155077119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.655 Γ— 10¹⁰⁰(101-digit number)
66557062407546901408…87278600830310154239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.331 Γ— 10¹⁰¹(102-digit number)
13311412481509380281…74557201660620308479
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:57,996,065 XPMΒ·at block #6,843,960 Β· updates every 60s
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