Block #601,490

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/25/2014, 2:22:46 PM · Difficulty 10.9143 · 6,195,088 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
436279a8ba771abaf06c1ba0d79567b7ef63fa1a0eb4d8a4f898f64f49283b14

Height

#601,490

Difficulty

10.914348

Transactions

5

Size

1.81 KB

Version

2

Bits

0aea12b2

Nonce

1,157,167,846

Timestamp

6/25/2014, 2:22:46 PM

Confirmations

6,195,088

Merkle Root

1f2cbaaf25cf167c700fcd12a0a91f2ee7cae61af855f970b18f74cbe9466c6e
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.

2.052 × 10⁹⁷(98-digit number)
20520996119789177235…71796300846449412399
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
2.052 × 10⁹⁷(98-digit number)
20520996119789177235…71796300846449412399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.104 × 10⁹⁷(98-digit number)
41041992239578354470…43592601692898824799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.208 × 10⁹⁷(98-digit number)
82083984479156708941…87185203385797649599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.641 × 10⁹⁸(99-digit number)
16416796895831341788…74370406771595299199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.283 × 10⁹⁸(99-digit number)
32833593791662683576…48740813543190598399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.566 × 10⁹⁸(99-digit number)
65667187583325367153…97481627086381196799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.313 × 10⁹⁹(100-digit number)
13133437516665073430…94963254172762393599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.626 × 10⁹⁹(100-digit number)
26266875033330146861…89926508345524787199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.253 × 10⁹⁹(100-digit number)
52533750066660293722…79853016691049574399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.050 × 10¹⁰⁰(101-digit number)
10506750013332058744…59706033382099148799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.101 × 10¹⁰⁰(101-digit number)
21013500026664117489…19412066764198297599
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:57,616,625 XPM·at block #6,796,577 · updates every 60s
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