Block #467,547

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/30/2014, 8:58:21 PM · Difficulty 10.4354 · 6,329,122 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f182f442f59850616f61f2a24208a7cdd706306b7711320874c74cda1016581a

Height

#467,547

Difficulty

10.435360

Transactions

2

Size

860 B

Version

2

Bits

0a6f73bc

Nonce

184,598

Timestamp

3/30/2014, 8:58:21 PM

Confirmations

6,329,122

Merkle Root

7b398bcb8abe429522f4719b61571b5ad867b54e2e5367a2ab75c7be51917992
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.

2.963 × 10¹⁰⁰(101-digit number)
29631587059976704050…93831882459324982799
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
2.963 × 10¹⁰⁰(101-digit number)
29631587059976704050…93831882459324982799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.926 × 10¹⁰⁰(101-digit number)
59263174119953408100…87663764918649965599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.185 × 10¹⁰¹(102-digit number)
11852634823990681620…75327529837299931199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.370 × 10¹⁰¹(102-digit number)
23705269647981363240…50655059674599862399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.741 × 10¹⁰¹(102-digit number)
47410539295962726480…01310119349199724799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
9.482 × 10¹⁰¹(102-digit number)
94821078591925452960…02620238698399449599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.896 × 10¹⁰²(103-digit number)
18964215718385090592…05240477396798899199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.792 × 10¹⁰²(103-digit number)
37928431436770181184…10480954793597798399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.585 × 10¹⁰²(103-digit number)
75856862873540362368…20961909587195596799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.517 × 10¹⁰³(104-digit number)
15171372574708072473…41923819174391193599
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:57,617,358 XPM·at block #6,796,668 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.