Block #594,664

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/19/2014, 4:50:59 PM · Difficulty 10.9382 · 6,209,034 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
21e646b5bd272b9affca1aaa95efe6b3ac8a0938d68108b89c4c11db19697160

Height

#594,664

Difficulty

10.938220

Transactions

1

Size

593 B

Version

2

Bits

0af02f2c

Nonce

236,132

Timestamp

6/19/2014, 4:50:59 PM

Confirmations

6,209,034

Merkle Root

5d3b57b3b5e8eaa9b8a769e0f80fa4c7e6f8b9e4ffb74897fecc13f99e2d5e70
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.

2.932 × 10⁹³(94-digit number)
29328649804051158744…56940578555480562559
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
2.932 × 10⁹³(94-digit number)
29328649804051158744…56940578555480562559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.865 × 10⁹³(94-digit number)
58657299608102317488…13881157110961125119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.173 × 10⁹⁴(95-digit number)
11731459921620463497…27762314221922250239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.346 × 10⁹⁴(95-digit number)
23462919843240926995…55524628443844500479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.692 × 10⁹⁴(95-digit number)
46925839686481853990…11049256887689000959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.385 × 10⁹⁴(95-digit number)
93851679372963707981…22098513775378001919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.877 × 10⁹⁵(96-digit number)
18770335874592741596…44197027550756003839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.754 × 10⁹⁵(96-digit number)
37540671749185483192…88394055101512007679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.508 × 10⁹⁵(96-digit number)
75081343498370966385…76788110203024015359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.501 × 10⁹⁶(97-digit number)
15016268699674193277…53576220406048030719
Verify on FactorDB ↗Wolfram Alpha ↗

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 — 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
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 × 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:57,673,622 XPM·at block #6,803,697 · updates every 60s
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