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Block #2,583,278

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/24/2018, 5:07:29 PM Β· Difficulty 11.1662 Β· 4,256,954 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
78e9c02a4b031ec4938e88ff3be68786eebe14a0c14f49e7c6cafd15112bf072
View on Chainz β†—

Height

#2,583,278

Difficulty

11.166220

Transactions

2

Size

575 B

Version

2

Bits

0b2a8d65

Nonce

173,529,774

Timestamp

3/24/2018, 5:07:29 PM

Confirmations

4,256,954

Mined by

⛏️ P2SHAY94A6DB478R7Agt8za5UTMfEtbeykb9Ba

Merkle Root

7e9b8a22dd3b575cbe39ee3c3317561a2c16e5948036746d1fcbe192b5e52a9e
Transactions (2)
Coinbase9036af28dbca13…7607e68d09d889
1 in β†’ 1 out8.0200 XPM110 B
AY94A6DB…beykb9Ba
cf6791005adab5…570bfded97d450
2 in β†’ 2 out55.8425 XPM374 B
AV8MfsV3…6Cjjy8PhALf5C94r…61airdGv
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.

2.409 Γ— 10⁹⁢(97-digit number)
24090895216221838313…06694522640092871679
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
2.409 Γ— 10⁹⁢(97-digit number)
24090895216221838313…06694522640092871679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.818 Γ— 10⁹⁢(97-digit number)
48181790432443676627…13389045280185743359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.636 Γ— 10⁹⁢(97-digit number)
96363580864887353254…26778090560371486719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.927 Γ— 10⁹⁷(98-digit number)
19272716172977470650…53556181120742973439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.854 Γ— 10⁹⁷(98-digit number)
38545432345954941301…07112362241485946879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.709 Γ— 10⁹⁷(98-digit number)
77090864691909882603…14224724482971893759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.541 Γ— 10⁹⁸(99-digit number)
15418172938381976520…28449448965943787519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.083 Γ— 10⁹⁸(99-digit number)
30836345876763953041…56898897931887575039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.167 Γ— 10⁹⁸(99-digit number)
61672691753527906082…13797795863775150079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.233 Γ— 10⁹⁹(100-digit number)
12334538350705581216…27595591727550300159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.466 Γ— 10⁹⁹(100-digit number)
24669076701411162433…55191183455100600319
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:57,966,166 XPMΒ·at block #6,840,231 Β· updates every 60s
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