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Block #2,160,760

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/14/2017, 7:44:06 PM Β· Difficulty 10.9017 Β· 4,666,078 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e54a38cf0f518c1ceb804594a68b175636f534f2cf35d7410112ec2d50d0ca57
View on Chainz β†—

Height

#2,160,760

Difficulty

10.901658

Transactions

2

Size

1.83 KB

Version

2

Bits

0ae6d30c

Nonce

1,574,702,209

Timestamp

6/14/2017, 7:44:06 PM

Confirmations

4,666,078

Mined by

⛏️ P2SHAeHCku7HBGduyYWka1kad6iuhXr27UnAUE

Merkle Root

ac038e820ad7e55ddb885eb0f74ee311b1058a7ad047535f6b8a1b1cfde69b26
Transactions (2)
Coinbasedf277960889dea…c4bc736166e965
1 in β†’ 1 out8.4200 XPM110 B
AeHCku7H…r27UnAUE
c4b39c739ef4e8…36ebe0b5ccd0b7
11 in β†’ 1 out1042.9900 XPM1.63 KB
AcxhUhX6…N8N8w2tm
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.

1.475 Γ— 10⁹⁢(97-digit number)
14758603039458307635…12444787029228889279
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
1.475 Γ— 10⁹⁢(97-digit number)
14758603039458307635…12444787029228889279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.951 Γ— 10⁹⁢(97-digit number)
29517206078916615270…24889574058457778559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.903 Γ— 10⁹⁢(97-digit number)
59034412157833230540…49779148116915557119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.180 Γ— 10⁹⁷(98-digit number)
11806882431566646108…99558296233831114239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.361 Γ— 10⁹⁷(98-digit number)
23613764863133292216…99116592467662228479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.722 Γ— 10⁹⁷(98-digit number)
47227529726266584432…98233184935324456959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.445 Γ— 10⁹⁷(98-digit number)
94455059452533168864…96466369870648913919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.889 Γ— 10⁹⁸(99-digit number)
18891011890506633772…92932739741297827839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.778 Γ— 10⁹⁸(99-digit number)
37782023781013267545…85865479482595655679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.556 Γ— 10⁹⁸(99-digit number)
75564047562026535091…71730958965191311359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,858,871 XPMΒ·at block #6,826,837 Β· updates every 60s
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