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Block #2,762,066

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/23/2018, 8:11:50 PM Β· Difficulty 11.6547 Β· 4,078,024 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4956437d3b26b04492eefa521935a4238c7eec5191c727c0b641534e619b1a29
View on Chainz β†—

Height

#2,762,066

Difficulty

11.654727

Transactions

2

Size

573 B

Version

2

Bits

0ba79c2e

Nonce

219,334,592

Timestamp

7/23/2018, 8:11:50 PM

Confirmations

4,078,024

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

08645bfc0986ab800f6711d21c6204b525e29042a0b9dd9034789840e33997a7
Transactions (2)
Coinbase246f166a1d49f2…5fd479c085576e
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
5e13a4e61fddb5…1164528a51387e
2 in β†’ 2 out44.2921 XPM373 B
AFpHJhDK…hyA1PvSQAJpWtkeK…5wnn3ofi
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.

6.188 Γ— 10⁹⁡(96-digit number)
61880138449485578174…61039764012081377279
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
6.188 Γ— 10⁹⁡(96-digit number)
61880138449485578174…61039764012081377279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.237 Γ— 10⁹⁢(97-digit number)
12376027689897115634…22079528024162754559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.475 Γ— 10⁹⁢(97-digit number)
24752055379794231269…44159056048325509119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.950 Γ— 10⁹⁢(97-digit number)
49504110759588462539…88318112096651018239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.900 Γ— 10⁹⁢(97-digit number)
99008221519176925079…76636224193302036479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.980 Γ— 10⁹⁷(98-digit number)
19801644303835385015…53272448386604072959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.960 Γ— 10⁹⁷(98-digit number)
39603288607670770031…06544896773208145919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.920 Γ— 10⁹⁷(98-digit number)
79206577215341540063…13089793546416291839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.584 Γ— 10⁹⁸(99-digit number)
15841315443068308012…26179587092832583679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.168 Γ— 10⁹⁸(99-digit number)
31682630886136616025…52359174185665167359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.336 Γ— 10⁹⁸(99-digit number)
63365261772273232050…04718348371330334719
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:57,965,030 XPMΒ·at block #6,840,089 Β· updates every 60s
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