Block #469,617

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/1/2014, 8:47:25 AM · Difficulty 10.4277 · 6,357,326 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
246ffa0a84823730470e60297db4d78928fff7353c08062bbafb729e61212e41

Height

#469,617

Difficulty

10.427665

Transactions

1

Size

970 B

Version

2

Bits

0a6d7b74

Nonce

6,891

Timestamp

4/1/2014, 8:47:25 AM

Confirmations

6,357,326

Merkle Root

0728cf995279f03bdb646eacf8abe1112e9c6c351d8fa221b80b53cfea38c3f6
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.

4.093 × 10⁹⁷(98-digit number)
40934250073500527136…46566840683099002879
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
4.093 × 10⁹⁷(98-digit number)
40934250073500527136…46566840683099002879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
8.186 × 10⁹⁷(98-digit number)
81868500147001054273…93133681366198005759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.637 × 10⁹⁸(99-digit number)
16373700029400210854…86267362732396011519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.274 × 10⁹⁸(99-digit number)
32747400058800421709…72534725464792023039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.549 × 10⁹⁸(99-digit number)
65494800117600843418…45069450929584046079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.309 × 10⁹⁹(100-digit number)
13098960023520168683…90138901859168092159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.619 × 10⁹⁹(100-digit number)
26197920047040337367…80277803718336184319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.239 × 10⁹⁹(100-digit number)
52395840094080674734…60555607436672368639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.047 × 10¹⁰⁰(101-digit number)
10479168018816134946…21111214873344737279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.095 × 10¹⁰⁰(101-digit number)
20958336037632269893…42222429746689474559
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:57,859,718 XPM·at block #6,826,942 · updates every 60s
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