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Block #2,722,785

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/26/2018, 10:23:04 PM Β· Difficulty 11.6148 Β· 4,122,309 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7bac9fe43cc3d3f2a8760712f5a2a69cb65cc63a33fbd6a2e606869771cdc93f
View on Chainz β†—

Height

#2,722,785

Difficulty

11.614819

Transactions

1

Size

200 B

Version

2

Bits

0b9d64cd

Nonce

346,692,283

Timestamp

6/26/2018, 10:23:04 PM

Confirmations

4,122,309

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

0f32ac1618b8fbdf1bf653a4a95e916cc13fb1b1cdaaa1f0edd226be55e93e86
Transactions (1)
Coinbase0f32ac1618b8fb…d226be55e93e86
1 in β†’ 1 out7.4000 XPM109 B
AZtxQr2F…7grUWrUz
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.

1.071 Γ— 10⁹⁢(97-digit number)
10710346436252246735…81975002306699263999
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
1.071 Γ— 10⁹⁢(97-digit number)
10710346436252246735…81975002306699263999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.142 Γ— 10⁹⁢(97-digit number)
21420692872504493471…63950004613398527999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.284 Γ— 10⁹⁢(97-digit number)
42841385745008986943…27900009226797055999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.568 Γ— 10⁹⁢(97-digit number)
85682771490017973886…55800018453594111999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.713 Γ— 10⁹⁷(98-digit number)
17136554298003594777…11600036907188223999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.427 Γ— 10⁹⁷(98-digit number)
34273108596007189554…23200073814376447999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.854 Γ— 10⁹⁷(98-digit number)
68546217192014379108…46400147628752895999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.370 Γ— 10⁹⁸(99-digit number)
13709243438402875821…92800295257505791999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.741 Γ— 10⁹⁸(99-digit number)
27418486876805751643…85600590515011583999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.483 Γ— 10⁹⁸(99-digit number)
54836973753611503287…71201181030023167999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.096 Γ— 10⁹⁹(100-digit number)
10967394750722300657…42402362060046335999
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:58,005,177 XPMΒ·at block #6,845,093 Β· updates every 60s
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