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Block #2,126,240

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/21/2017, 2:46:45 AM Β· Difficulty 10.9194 Β· 4,717,022 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e48b4d7df0cc2d7ba8ec4ef3a6127b5d1da0939cf133656b09e62681b5abf756
View on Chainz β†—

Height

#2,126,240

Difficulty

10.919379

Transactions

1

Size

199 B

Version

2

Bits

0aeb5c72

Nonce

464,703,330

Timestamp

5/21/2017, 2:46:45 AM

Confirmations

4,717,022

Mined by

⛏️ P2SHAUdcEjVJKjY2t7pQWZrt655t6jdhpycaKZ

Merkle Root

ef9a8aab06062b35c7b09fb23d023712a76c4779dbb000a3207ec6525e892d6d
Transactions (1)
Coinbaseef9a8aab06062b…7ec6525e892d6d
1 in β†’ 1 out8.3700 XPM109 B
AUdcEjVJ…dhpycaKZ
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.

1.057 Γ— 10⁹⁴(95-digit number)
10579343307951716834…32310200672355707279
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
1.057 Γ— 10⁹⁴(95-digit number)
10579343307951716834…32310200672355707279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.115 Γ— 10⁹⁴(95-digit number)
21158686615903433668…64620401344711414559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.231 Γ— 10⁹⁴(95-digit number)
42317373231806867337…29240802689422829119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.463 Γ— 10⁹⁴(95-digit number)
84634746463613734675…58481605378845658239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.692 Γ— 10⁹⁡(96-digit number)
16926949292722746935…16963210757691316479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.385 Γ— 10⁹⁡(96-digit number)
33853898585445493870…33926421515382632959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.770 Γ— 10⁹⁡(96-digit number)
67707797170890987740…67852843030765265919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.354 Γ— 10⁹⁢(97-digit number)
13541559434178197548…35705686061530531839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.708 Γ— 10⁹⁢(97-digit number)
27083118868356395096…71411372123061063679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.416 Γ— 10⁹⁢(97-digit number)
54166237736712790192…42822744246122127359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.083 Γ— 10⁹⁷(98-digit number)
10833247547342558038…85645488492244254719
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:57,990,469 XPMΒ·at block #6,843,261 Β· updates every 60s
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