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Block #2,761,926

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/23/2018, 5:56:32 PM Β· Difficulty 11.6545 Β· 4,076,877 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
87bacb8afb4a115d30cfdb7fb665a7c0b1099d305a29ff2586fbfc9914594402
View on Chainz β†—

Height

#2,761,926

Difficulty

11.654521

Transactions

2

Size

1.36 KB

Version

2

Bits

0ba78eb0

Nonce

1,168,233,220

Timestamp

7/23/2018, 5:56:32 PM

Confirmations

4,076,877

Mined by

⛏️ P2SHAX26Pdq8YQfnn61NFJ6tGhWc1oGhQ92zqD

Merkle Root

527a45b25c7a58a7249a14e11fec88e92b5ed5ce086ea88a3aa48409a424842d
Transactions (2)
Coinbase01e14bfb887838…e2ac381dc88a9e
1 in β†’ 1 out7.3700 XPM110 B
AX26Pdq8…GhQ92zqD
f7a68f6c95f42b…6131db55868858
8 in β†’ 2 out20.0209 XPM1.17 KB
AWu6SVKR…fD2XKYmkAHr6Datf…GxroLH9G
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.

3.087 Γ— 10⁹⁴(95-digit number)
30871916508765622324…59959448909559763199
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
3.087 Γ— 10⁹⁴(95-digit number)
30871916508765622324…59959448909559763199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.174 Γ— 10⁹⁴(95-digit number)
61743833017531244649…19918897819119526399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.234 Γ— 10⁹⁡(96-digit number)
12348766603506248929…39837795638239052799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.469 Γ— 10⁹⁡(96-digit number)
24697533207012497859…79675591276478105599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.939 Γ— 10⁹⁡(96-digit number)
49395066414024995719…59351182552956211199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.879 Γ— 10⁹⁡(96-digit number)
98790132828049991439…18702365105912422399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.975 Γ— 10⁹⁢(97-digit number)
19758026565609998287…37404730211824844799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.951 Γ— 10⁹⁢(97-digit number)
39516053131219996575…74809460423649689599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.903 Γ— 10⁹⁢(97-digit number)
79032106262439993151…49618920847299379199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.580 Γ— 10⁹⁷(98-digit number)
15806421252487998630…99237841694598758399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.161 Γ— 10⁹⁷(98-digit number)
31612842504975997260…98475683389197516799
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:57,954,689 XPMΒ·at block #6,838,802 Β· updates every 60s
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