Block #1,924,536

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/5/2017, 5:13:27 AM · Difficulty 10.7219 · 4,912,283 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
22a8a21bb764b494cdfdd8c1276c97ccacd2fa11fb2dc1c713e0339183ff22c5

Height

#1,924,536

Difficulty

10.721888

Transactions

2

Size

1.14 KB

Version

2

Bits

0ab8cdac

Nonce

209,159,058

Timestamp

1/5/2017, 5:13:27 AM

Confirmations

4,912,283

Merkle Root

3e4c01e8308b5a9e8c45fcd5b7aaa21bd779ff301174709212bec919365e64ef
Transactions (2)
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.

2.478 × 10⁹⁶(97-digit number)
24782445794394660341…34128053785051356161
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
2.478 × 10⁹⁶(97-digit number)
24782445794394660341…34128053785051356161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.956 × 10⁹⁶(97-digit number)
49564891588789320683…68256107570102712321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.912 × 10⁹⁶(97-digit number)
99129783177578641367…36512215140205424641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.982 × 10⁹⁷(98-digit number)
19825956635515728273…73024430280410849281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.965 × 10⁹⁷(98-digit number)
39651913271031456546…46048860560821698561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.930 × 10⁹⁷(98-digit number)
79303826542062913093…92097721121643397121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.586 × 10⁹⁸(99-digit number)
15860765308412582618…84195442243286794241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.172 × 10⁹⁸(99-digit number)
31721530616825165237…68390884486573588481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.344 × 10⁹⁸(99-digit number)
63443061233650330475…36781768973147176961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.268 × 10⁹⁹(100-digit number)
12688612246730066095…73563537946294353921
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:57,938,836 XPM·at block #6,836,818 · updates every 60s
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