Block #2,320,954

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/3/2017, 3:03:51 PM · Difficulty 10.9204 · 4,518,822 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
854483775c24d7674a461e2898e8263be031eb669caa6f92123ebc350aee969a

Height

#2,320,954

Difficulty

10.920441

Transactions

2

Size

1.72 KB

Version

2

Bits

0aeba209

Nonce

1,608,937,547

Timestamp

10/3/2017, 3:03:51 PM

Confirmations

4,518,822

Merkle Root

36ff87510ca9a78fb57829306cbee8c224221f7813c78aaee3ba51b38d60be48
Transactions (2)
1 in → 1 out8.3900 XPM110 B
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.

2.922 × 10⁹⁶(97-digit number)
29224570025905489540…22520606540845895681
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
2.922 × 10⁹⁶(97-digit number)
29224570025905489540…22520606540845895681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.844 × 10⁹⁶(97-digit number)
58449140051810979080…45041213081691791361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.168 × 10⁹⁷(98-digit number)
11689828010362195816…90082426163383582721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.337 × 10⁹⁷(98-digit number)
23379656020724391632…80164852326767165441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.675 × 10⁹⁷(98-digit number)
46759312041448783264…60329704653534330881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.351 × 10⁹⁷(98-digit number)
93518624082897566529…20659409307068661761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.870 × 10⁹⁸(99-digit number)
18703724816579513305…41318818614137323521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.740 × 10⁹⁸(99-digit number)
37407449633159026611…82637637228274647041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.481 × 10⁹⁸(99-digit number)
74814899266318053223…65275274456549294081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.496 × 10⁹⁹(100-digit number)
14962979853263610644…30550548913098588161
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:57,962,498 XPM·at block #6,839,775 · updates every 60s
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