Block #2,174,601

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/24/2017, 12:15:25 AM · Difficulty 10.9132 · 4,668,166 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
da98774896e6fc9e2ed053b10e65bbf37e9f23f8f14e9bd159fe402ea3b6c0a8

Height

#2,174,601

Difficulty

10.913243

Transactions

2

Size

1.14 KB

Version

2

Bits

0ae9ca51

Nonce

134,553,011

Timestamp

6/24/2017, 12:15:25 AM

Confirmations

4,668,166

Merkle Root

7775c7ac3e3f7e2c9a2b0b3f9ac796c3c48791745a63ca4d895b203c1813c431
Transactions (2)
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.213 × 10⁹⁷(98-digit number)
12139603730964507917…95085494515473356799
Discovered Prime Numbers
p_k = 2^k × origin − 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 − 1
1.213 × 10⁹⁷(98-digit number)
12139603730964507917…95085494515473356799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.427 × 10⁹⁷(98-digit number)
24279207461929015834…90170989030946713599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.855 × 10⁹⁷(98-digit number)
48558414923858031668…80341978061893427199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.711 × 10⁹⁷(98-digit number)
97116829847716063337…60683956123786854399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.942 × 10⁹⁸(99-digit number)
19423365969543212667…21367912247573708799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.884 × 10⁹⁸(99-digit number)
38846731939086425334…42735824495147417599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.769 × 10⁹⁸(99-digit number)
77693463878172850669…85471648990294835199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.553 × 10⁹⁹(100-digit number)
15538692775634570133…70943297980589670399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.107 × 10⁹⁹(100-digit number)
31077385551269140267…41886595961179340799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.215 × 10⁹⁹(100-digit number)
62154771102538280535…83773191922358681599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.243 × 10¹⁰⁰(101-digit number)
12430954220507656107…67546383844717363199
Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★☆☆
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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,986,475 XPM·at block #6,842,766 · updates every 60s
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