Block #206,577

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/12/2013, 9:40:58 PM · Difficulty 9.9013 · 6,619,749 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d703030f6125039e904e0e3c4fd409a7f41fbd720cdb11831f9ea63685a5fefd

Height

#206,577

Difficulty

9.901297

Transactions

5

Size

2.38 KB

Version

2

Bits

09e6bb6a

Nonce

14,517

Timestamp

10/12/2013, 9:40:58 PM

Confirmations

6,619,749

Merkle Root

4409d57671b5023df8873d9f69beb41e6d3b024b5c0be7d273ba95a248706503
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.

2.311 × 10¹⁰⁷(108-digit number)
23115814184988845043…37876287395264278379
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
2.311 × 10¹⁰⁷(108-digit number)
23115814184988845043…37876287395264278379
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.623 × 10¹⁰⁷(108-digit number)
46231628369977690086…75752574790528556759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.246 × 10¹⁰⁷(108-digit number)
92463256739955380172…51505149581057113519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.849 × 10¹⁰⁸(109-digit number)
18492651347991076034…03010299162114227039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.698 × 10¹⁰⁸(109-digit number)
36985302695982152068…06020598324228454079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.397 × 10¹⁰⁸(109-digit number)
73970605391964304137…12041196648456908159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.479 × 10¹⁰⁹(110-digit number)
14794121078392860827…24082393296913816319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.958 × 10¹⁰⁹(110-digit number)
29588242156785721655…48164786593827632639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.917 × 10¹⁰⁹(110-digit number)
59176484313571443310…96329573187655265279
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,854,748 XPM·at block #6,826,325 · updates every 60s
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