Block #362,600

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/16/2014, 7:58:18 PM · Difficulty 10.4153 · 6,429,567 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8dbf18aa7796fb4773841fb9f4e98b8cca51f758a15a36bfd09e9ee08f43b5b7

Height

#362,600

Difficulty

10.415269

Transactions

4

Size

4.76 KB

Version

2

Bits

0a6a4f0b

Nonce

148,503

Timestamp

1/16/2014, 7:58:18 PM

Confirmations

6,429,567

Merkle Root

86b979436332ede5a6b73239f8fad9fa434298d915a0b4e21590e0b63c9b5c69
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.

1.278 × 10¹⁰⁵(106-digit number)
12787226226336070691…08889569091552870399
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
1.278 × 10¹⁰⁵(106-digit number)
12787226226336070691…08889569091552870399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.557 × 10¹⁰⁵(106-digit number)
25574452452672141383…17779138183105740799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.114 × 10¹⁰⁵(106-digit number)
51148904905344282767…35558276366211481599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.022 × 10¹⁰⁶(107-digit number)
10229780981068856553…71116552732422963199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.045 × 10¹⁰⁶(107-digit number)
20459561962137713106…42233105464845926399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.091 × 10¹⁰⁶(107-digit number)
40919123924275426213…84466210929691852799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.183 × 10¹⁰⁶(107-digit number)
81838247848550852427…68932421859383705599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.636 × 10¹⁰⁷(108-digit number)
16367649569710170485…37864843718767411199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.273 × 10¹⁰⁷(108-digit number)
32735299139420340970…75729687437534822399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.547 × 10¹⁰⁷(108-digit number)
65470598278840681941…51459374875069644799
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:57,581,291 XPM·at block #6,792,166 · 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.