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Block #2,833,197

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/10/2018, 2:16:34 PM Β· Difficulty 11.7148 Β· 4,009,830 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8ebd8a88d55eb96768b89dd77c1a49ceac6525564dde07c847e3102efc81251c
View on Chainz β†—

Height

#2,833,197

Difficulty

11.714790

Transactions

1

Size

200 B

Version

2

Bits

0bb6fc72

Nonce

138,330,357

Timestamp

9/10/2018, 2:16:34 PM

Confirmations

4,009,830

Mined by

⛏️ P2SHAZZT8qnYust46RgWn8oS6L7xEmTgwn8DJX

Merkle Root

dceda43cec584bfbbac3aed2b2507c2b22036d2956b5adf35751e63160f3ae3a
Transactions (1)
Coinbasedceda43cec584b…51e63160f3ae3a
1 in β†’ 1 out7.2700 XPM110 B
AZZT8qnY…Tgwn8DJX
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.

1.012 Γ— 10⁹⁡(96-digit number)
10124615937450329030…64601484452963583999
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
1.012 Γ— 10⁹⁡(96-digit number)
10124615937450329030…64601484452963583999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.024 Γ— 10⁹⁡(96-digit number)
20249231874900658061…29202968905927167999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.049 Γ— 10⁹⁡(96-digit number)
40498463749801316122…58405937811854335999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.099 Γ— 10⁹⁡(96-digit number)
80996927499602632245…16811875623708671999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.619 Γ— 10⁹⁢(97-digit number)
16199385499920526449…33623751247417343999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.239 Γ— 10⁹⁢(97-digit number)
32398770999841052898…67247502494834687999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.479 Γ— 10⁹⁢(97-digit number)
64797541999682105796…34495004989669375999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.295 Γ— 10⁹⁷(98-digit number)
12959508399936421159…68990009979338751999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.591 Γ— 10⁹⁷(98-digit number)
25919016799872842318…37980019958677503999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.183 Γ— 10⁹⁷(98-digit number)
51838033599745684637…75960039917355007999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.036 Γ— 10⁹⁸(99-digit number)
10367606719949136927…51920079834710015999
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:57,988,570 XPMΒ·at block #6,843,026 Β· updates every 60s
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