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Block #2,770,784

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 7/29/2018, 8:25:42 PM Β· Difficulty 11.6593 Β· 4,073,768 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1591d2cab9ee7aaa3cb9f0a40e0350e75d1ac2349ccfb03b445ba49fa7f8f62a
View on Chainz β†—

Height

#2,770,784

Difficulty

11.659331

Transactions

1

Size

200 B

Version

2

Bits

0ba8c9e7

Nonce

1,414,838,059

Timestamp

7/29/2018, 8:25:42 PM

Confirmations

4,073,768

Mined by

⛏️ P2SHAaeWwoNkLKenx2bXhxCXCeM46oLTaLKbBQ

Merkle Root

503459ff2cc878d6b957fbb644d0eab7cbc672a13d0b9e790a1f8831a46bad19
Transactions (1)
Coinbase503459ff2cc878…1f8831a46bad19
1 in β†’ 1 out7.3400 XPM110 B
AaeWwoNk…LTaLKbBQ
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.

8.976 Γ— 10⁹³(94-digit number)
89765585777416297479…98647570993633772799
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
8.976 Γ— 10⁹³(94-digit number)
89765585777416297479…98647570993633772799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.795 Γ— 10⁹⁴(95-digit number)
17953117155483259495…97295141987267545599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.590 Γ— 10⁹⁴(95-digit number)
35906234310966518991…94590283974535091199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.181 Γ— 10⁹⁴(95-digit number)
71812468621933037983…89180567949070182399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.436 Γ— 10⁹⁡(96-digit number)
14362493724386607596…78361135898140364799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.872 Γ— 10⁹⁡(96-digit number)
28724987448773215193…56722271796280729599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.744 Γ— 10⁹⁡(96-digit number)
57449974897546430386…13444543592561459199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.148 Γ— 10⁹⁢(97-digit number)
11489994979509286077…26889087185122918399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.297 Γ— 10⁹⁢(97-digit number)
22979989959018572154…53778174370245836799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.595 Γ— 10⁹⁢(97-digit number)
45959979918037144309…07556348740491673599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.191 Γ— 10⁹⁢(97-digit number)
91919959836074288619…15112697480983347199
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:58,000,819 XPMΒ·at block #6,844,551 Β· updates every 60s
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