Block #922,471

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/4/2015, 12:21:03 PM · Difficulty 10.9153 · 5,871,880 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
64ad84ff926a928a435a3a8169f37e6c5f6c2e82955a6604d13765a723e46be2

Height

#922,471

Difficulty

10.915265

Transactions

5

Size

116.04 KB

Version

2

Bits

0aea4ecb

Nonce

989,549,965

Timestamp

2/4/2015, 12:21:03 PM

Confirmations

5,871,880

Merkle Root

6dec5297a04232349acbd206b7561ec584f2ab0b325fa3ecb95c258311f9795d
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out993.2804 XPM28.96 KB
200 in → 1 out903.5996 XPM28.96 KB
200 in → 1 out1101.4737 XPM28.96 KB
200 in → 1 out953.9890 XPM28.96 KB
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.

3.127 × 10⁹⁶(97-digit number)
31273382395688471913…79787667156921548801
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
3.127 × 10⁹⁶(97-digit number)
31273382395688471913…79787667156921548801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.254 × 10⁹⁶(97-digit number)
62546764791376943826…59575334313843097601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.250 × 10⁹⁷(98-digit number)
12509352958275388765…19150668627686195201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.501 × 10⁹⁷(98-digit number)
25018705916550777530…38301337255372390401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.003 × 10⁹⁷(98-digit number)
50037411833101555061…76602674510744780801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.000 × 10⁹⁸(99-digit number)
10007482366620311012…53205349021489561601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.001 × 10⁹⁸(99-digit number)
20014964733240622024…06410698042979123201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.002 × 10⁹⁸(99-digit number)
40029929466481244049…12821396085958246401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.005 × 10⁹⁸(99-digit number)
80059858932962488098…25642792171916492801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.601 × 10⁹⁹(100-digit number)
16011971786592497619…51285584343832985601
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:57,598,841 XPM·at block #6,794,350 · updates every 60s
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