Block #602,713

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/26/2014, 12:04:19 PM · Difficulty 10.9131 · 6,202,518 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
074af4fee1a3ed584adc8480d38ec34167879f982c3b18af32fe75b0d8770735

Height

#602,713

Difficulty

10.913058

Transactions

5

Size

1.05 KB

Version

2

Bits

0ae9be2b

Nonce

1,789,632

Timestamp

6/26/2014, 12:04:19 PM

Confirmations

6,202,518

Merkle Root

805e8a54ff42f5cc638cf3892dcf034c3b609367f4dad27e5681bc08f6a8e3e9
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.

1.434 × 10⁹⁹(100-digit number)
14349337275083155767…87898350482554879999
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
1.434 × 10⁹⁹(100-digit number)
14349337275083155767…87898350482554879999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.869 × 10⁹⁹(100-digit number)
28698674550166311534…75796700965109759999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.739 × 10⁹⁹(100-digit number)
57397349100332623069…51593401930219519999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.147 × 10¹⁰⁰(101-digit number)
11479469820066524613…03186803860439039999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.295 × 10¹⁰⁰(101-digit number)
22958939640133049227…06373607720878079999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.591 × 10¹⁰⁰(101-digit number)
45917879280266098455…12747215441756159999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.183 × 10¹⁰⁰(101-digit number)
91835758560532196911…25494430883512319999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.836 × 10¹⁰¹(102-digit number)
18367151712106439382…50988861767024639999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.673 × 10¹⁰¹(102-digit number)
36734303424212878764…01977723534049279999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.346 × 10¹⁰¹(102-digit number)
73468606848425757528…03955447068098559999
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:57,685,921 XPM·at block #6,805,230 · updates every 60s
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