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Block #2,571,179

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/17/2018, 9:22:43 PM Β· Difficulty 10.9946 Β· 4,271,035 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d190e20d6c326b1a3323927430d35c073151d572704ce155998c0ae9d9defcb2
View on Chainz β†—

Height

#2,571,179

Difficulty

10.994603

Transactions

1

Size

200 B

Version

2

Bits

0afe9e47

Nonce

89,983,588

Timestamp

3/17/2018, 9:22:43 PM

Confirmations

4,271,035

Mined by

⛏️ P2SHAHp1hQVWiuufLch8cU47s5X5Fk5Rw9uZC5

Merkle Root

e58d269d339ae491f9a2ab3190d2fccefda65d922b3a2866b15f7d2777c9e7f3
Transactions (1)
Coinbasee58d269d339ae4…5f7d2777c9e7f3
1 in β†’ 1 out8.2600 XPM109 B
AHp1hQVW…5Rw9uZC5
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.

1.653 Γ— 10⁹⁢(97-digit number)
16533869871891971637…99900467425718513279
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
1.653 Γ— 10⁹⁢(97-digit number)
16533869871891971637…99900467425718513279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.306 Γ— 10⁹⁢(97-digit number)
33067739743783943274…99800934851437026559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.613 Γ— 10⁹⁢(97-digit number)
66135479487567886549…99601869702874053119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.322 Γ— 10⁹⁷(98-digit number)
13227095897513577309…99203739405748106239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.645 Γ— 10⁹⁷(98-digit number)
26454191795027154619…98407478811496212479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.290 Γ— 10⁹⁷(98-digit number)
52908383590054309239…96814957622992424959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.058 Γ— 10⁹⁸(99-digit number)
10581676718010861847…93629915245984849919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.116 Γ— 10⁹⁸(99-digit number)
21163353436021723695…87259830491969699839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.232 Γ— 10⁹⁸(99-digit number)
42326706872043447391…74519660983939399679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.465 Γ— 10⁹⁸(99-digit number)
84653413744086894783…49039321967878799359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.693 Γ— 10⁹⁹(100-digit number)
16930682748817378956…98078643935757598719
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:57,982,109 XPMΒ·at block #6,842,213 Β· updates every 60s
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