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Block #2,759,859

1CCLength 13β˜…β˜…β˜…β˜…β˜…

Cunningham Chain of the First Kind Β· Discovered 7/22/2018, 6:21:57 AM Β· Difficulty 11.6589 Β· 4,084,181 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
868e499a6028e4a765835d142b0077401acc4442dc64e119dab5decc0feca4f6
View on Chainz β†—

Height

#2,759,859

Difficulty

11.658921

Transactions

2

Size

390 B

Version

2

Bits

0ba8af08

Nonce

1,355,588,456

Timestamp

7/22/2018, 6:21:57 AM

Confirmations

4,084,181

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

d890fc654e409edd8741f9ed9b41a4b4dd910363a57509fe12a63aa31836b5f4
Transactions (2)
Coinbase0e1d053663d930…0ef6a12b2f136c
1 in β†’ 1 out7.3500 XPM109 B
AZtxQr2F…7grUWrUz
f2d65ab61cb868…b99119b607fb10
1 in β†’ 2 out7.3300 XPM192 B
Ack1CHDE…QdxM6gUyAdGFnV3a…o6n2zX3x
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.

1.744 Γ— 10⁹²(93-digit number)
17449497346527836504…58139071674499174199
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
1.744 Γ— 10⁹²(93-digit number)
17449497346527836504…58139071674499174199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.489 Γ— 10⁹²(93-digit number)
34898994693055673009…16278143348998348399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.979 Γ— 10⁹²(93-digit number)
69797989386111346018…32556286697996696799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.395 Γ— 10⁹³(94-digit number)
13959597877222269203…65112573395993393599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.791 Γ— 10⁹³(94-digit number)
27919195754444538407…30225146791986787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.583 Γ— 10⁹³(94-digit number)
55838391508889076814…60450293583973574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.116 Γ— 10⁹⁴(95-digit number)
11167678301777815362…20900587167947148799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.233 Γ— 10⁹⁴(95-digit number)
22335356603555630725…41801174335894297599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.467 Γ— 10⁹⁴(95-digit number)
44670713207111261451…83602348671788595199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.934 Γ— 10⁹⁴(95-digit number)
89341426414222522903…67204697343577190399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.786 Γ— 10⁹⁡(96-digit number)
17868285282844504580…34409394687154380799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
12
2^11 Γ— origin βˆ’ 1
3.573 Γ— 10⁹⁡(96-digit number)
35736570565689009161…68818789374308761599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
13
2^12 Γ— origin βˆ’ 1
7.147 Γ— 10⁹⁡(96-digit number)
71473141131378018323…37637578748617523199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 13 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
LegendaryChain length 13

Roughly 1 in 100,000 blocks. Extremely rare β€” celebrated by the community.

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:57,996,689 XPMΒ·at block #6,844,039 Β· updates every 60s
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