Block #207,449

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/13/2013, 11:06:13 AM · Difficulty 9.9026 · 6,595,618 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
4cb3c22c97fbc637ec8feb464c15794c25e9a27e876a72b134f19ef824fffad8

Height

#207,449

Difficulty

9.902636

Transactions

2

Size

787 B

Version

2

Bits

09e71322

Nonce

5,764

Timestamp

10/13/2013, 11:06:13 AM

Confirmations

6,595,618

Merkle Root

4371a1d8b7f1f25783514dfa09fee1fe836bdf8887ced8378de63a444aef9d16
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.

8.675 × 10⁸⁹(90-digit number)
86753593487761236613…99437438482580761749
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
8.675 × 10⁸⁹(90-digit number)
86753593487761236613…99437438482580761749
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.735 × 10⁹⁰(91-digit number)
17350718697552247322…98874876965161523499
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.470 × 10⁹⁰(91-digit number)
34701437395104494645…97749753930323046999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.940 × 10⁹⁰(91-digit number)
69402874790208989290…95499507860646093999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.388 × 10⁹¹(92-digit number)
13880574958041797858…90999015721292187999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.776 × 10⁹¹(92-digit number)
27761149916083595716…81998031442584375999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.552 × 10⁹¹(92-digit number)
55522299832167191432…63996062885168751999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.110 × 10⁹²(93-digit number)
11104459966433438286…27992125770337503999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.220 × 10⁹²(93-digit number)
22208919932866876573…55984251540675007999
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:57,668,565 XPM·at block #6,803,066 · updates every 60s
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