Block #1,951,604

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/23/2017, 10:31:26 PM · Difficulty 10.7291 · 4,863,375 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d509bbdcc7d3fc47bfe48bb7d2cae2f1f1aae7c1a82f9d38c5098d7cef617e7b

Height

#1,951,604

Difficulty

10.729133

Transactions

3

Size

1.08 KB

Version

2

Bits

0abaa877

Nonce

1,549,389,060

Timestamp

1/23/2017, 10:31:26 PM

Confirmations

4,863,375

Merkle Root

e8922aab4f108862745017c65a9c1d3686b23e21bd1d865085a02a905e67c211
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.

7.118 × 10⁹³(94-digit number)
71183958586940359585…46734793746853868281
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
7.118 × 10⁹³(94-digit number)
71183958586940359585…46734793746853868281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.423 × 10⁹⁴(95-digit number)
14236791717388071917…93469587493707736561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.847 × 10⁹⁴(95-digit number)
28473583434776143834…86939174987415473121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.694 × 10⁹⁴(95-digit number)
56947166869552287668…73878349974830946241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.138 × 10⁹⁵(96-digit number)
11389433373910457533…47756699949661892481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.277 × 10⁹⁵(96-digit number)
22778866747820915067…95513399899323784961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.555 × 10⁹⁵(96-digit number)
45557733495641830134…91026799798647569921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.111 × 10⁹⁵(96-digit number)
91115466991283660269…82053599597295139841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.822 × 10⁹⁶(97-digit number)
18223093398256732053…64107199194590279681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.644 × 10⁹⁶(97-digit number)
36446186796513464107…28214398389180559361
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:57,763,919 XPM·at block #6,814,978 · updates every 60s
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