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Block #2,095,079

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/1/2017, 1:30:41 AM Β· Difficulty 10.8720 Β· 4,743,930 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aa74048bfbba52f754cec249bb7b16ee1e900c9ad69898bb25bd876d66c68400
View on Chainz β†—

Height

#2,095,079

Difficulty

10.871950

Transactions

2

Size

1.28 KB

Version

2

Bits

0adf3822

Nonce

273,280,275

Timestamp

5/1/2017, 1:30:41 AM

Confirmations

4,743,930

Mined by

⛏️ P2SHASCqV5EWNUKDYrMwYoHMvRudMXxHzLUEmW

Merkle Root

6b733aebaebc241837ad095d28dd880c5fc9adde123c674d96802d91828c1d31
Transactions (2)
Coinbasefa6da350af8b81…0becfb48113c04
1 in β†’ 1 out8.4700 XPM109 B
ASCqV5EW…xHzLUEmW
21c1c4b1d7c7c1…2f730c12527494
7 in β†’ 2 out10000.0000 XPM1.09 KB
AWFYixUG…4nL4F5BpAVykG1qi…G9wYC7hP
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.

1.315 Γ— 10⁹⁷(98-digit number)
13150071036745110534…90745779505310924799
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
1.315 Γ— 10⁹⁷(98-digit number)
13150071036745110534…90745779505310924799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.630 Γ— 10⁹⁷(98-digit number)
26300142073490221069…81491559010621849599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.260 Γ— 10⁹⁷(98-digit number)
52600284146980442139…62983118021243699199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.052 Γ— 10⁹⁸(99-digit number)
10520056829396088427…25966236042487398399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.104 Γ— 10⁹⁸(99-digit number)
21040113658792176855…51932472084974796799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.208 Γ— 10⁹⁸(99-digit number)
42080227317584353711…03864944169949593599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.416 Γ— 10⁹⁸(99-digit number)
84160454635168707423…07729888339899187199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.683 Γ— 10⁹⁹(100-digit number)
16832090927033741484…15459776679798374399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.366 Γ— 10⁹⁹(100-digit number)
33664181854067482969…30919553359596748799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.732 Γ— 10⁹⁹(100-digit number)
67328363708134965938…61839106719193497599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.346 Γ— 10¹⁰⁰(101-digit number)
13465672741626993187…23678213438386995199
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:57,956,338 XPMΒ·at block #6,839,008 Β· updates every 60s
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