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Block #2,611,450

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/13/2018, 1:40:53 AM Β· Difficulty 11.2154 Β· 4,219,790 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
303d34b95cf9b7f2355aa032c35301f9a5d52f938868524b9b293fc52b660dd5
View on Chainz β†—

Height

#2,611,450

Difficulty

11.215394

Transactions

2

Size

20.92 KB

Version

2

Bits

0b372412

Nonce

834,045,696

Timestamp

4/13/2018, 1:40:53 AM

Confirmations

4,219,790

Mined by

⛏️ P2SHAGLX4oJFjYYswznviLbACUaNdAa2uXD1eM

Merkle Root

e0fd7bfdb19cc14c76fef9b0ef9ee2176ab956d6c2cd315151d91d2a2a3e2641
Transactions (2)
Coinbase73bf157cfc08de…81c3a69f0242ec
1 in β†’ 1 out8.1600 XPM109 B
AGLX4oJF…a2uXD1eM
1d4596ef3911a1…7e99bd16046933
143 in β†’ 2 out1436.7116 XPM20.73 KB
ATsGpLaK…6ivo8bfZARcKMnmT…5BLzvoTF
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.

8.445 Γ— 10⁹²(93-digit number)
84456143199737689647…38722091857524887679
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
8.445 Γ— 10⁹²(93-digit number)
84456143199737689647…38722091857524887679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.689 Γ— 10⁹³(94-digit number)
16891228639947537929…77444183715049775359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.378 Γ— 10⁹³(94-digit number)
33782457279895075859…54888367430099550719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.756 Γ— 10⁹³(94-digit number)
67564914559790151718…09776734860199101439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.351 Γ— 10⁹⁴(95-digit number)
13512982911958030343…19553469720398202879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.702 Γ— 10⁹⁴(95-digit number)
27025965823916060687…39106939440796405759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.405 Γ— 10⁹⁴(95-digit number)
54051931647832121374…78213878881592811519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.081 Γ— 10⁹⁡(96-digit number)
10810386329566424274…56427757763185623039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.162 Γ— 10⁹⁡(96-digit number)
21620772659132848549…12855515526371246079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.324 Γ— 10⁹⁡(96-digit number)
43241545318265697099…25711031052742492159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
8.648 Γ— 10⁹⁡(96-digit number)
86483090636531394199…51422062105484984319
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:57,894,069 XPMΒ·at block #6,831,239 Β· updates every 60s
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