Block #371,477

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/22/2014, 9:25:40 PM · Difficulty 10.4357 · 6,436,327 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
856ed475f35b01940a23ebc96a6c9e852110c20fb04da5481fc39195cdef586b

Height

#371,477

Difficulty

10.435748

Transactions

3

Size

920 B

Version

2

Bits

0a6f8d2a

Nonce

23,747

Timestamp

1/22/2014, 9:25:40 PM

Confirmations

6,436,327

Merkle Root

235ea658155f3dd847e4ef2e1d6c8fb924be69bc643c82f4a44082eac8041403
Transactions (3)
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.

5.353 × 10⁹⁸(99-digit number)
53536040002386452749…01694008706727140001
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
5.353 × 10⁹⁸(99-digit number)
53536040002386452749…01694008706727140001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.070 × 10⁹⁹(100-digit number)
10707208000477290549…03388017413454280001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.141 × 10⁹⁹(100-digit number)
21414416000954581099…06776034826908560001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.282 × 10⁹⁹(100-digit number)
42828832001909162199…13552069653817120001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.565 × 10⁹⁹(100-digit number)
85657664003818324399…27104139307634240001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.713 × 10¹⁰⁰(101-digit number)
17131532800763664879…54208278615268480001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.426 × 10¹⁰⁰(101-digit number)
34263065601527329759…08416557230536960001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.852 × 10¹⁰⁰(101-digit number)
68526131203054659519…16833114461073920001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.370 × 10¹⁰¹(102-digit number)
13705226240610931903…33666228922147840001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.741 × 10¹⁰¹(102-digit number)
27410452481221863807…67332457844295680001
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,706,466 XPM·at block #6,807,803 · updates every 60s
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