Block #2,494,232

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/28/2018, 10:41:25 AM · Difficulty 10.9731 · 4,339,573 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9a26e96d32366cf7037ec52964e450672a4ae139fd2a7d0797a0d217788ebba5

Height

#2,494,232

Difficulty

10.973072

Transactions

2

Size

426 B

Version

2

Bits

0af91b45

Nonce

261,778,972

Timestamp

1/28/2018, 10:41:25 AM

Confirmations

4,339,573

Merkle Root

0f4f2d34e4628b7f07df78fa658967ea5a3b3925b36dd9d0fdf1d589635700c9
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.

3.741 × 10⁹⁴(95-digit number)
37412732887302140774…65618864491086655361
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
3.741 × 10⁹⁴(95-digit number)
37412732887302140774…65618864491086655361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.482 × 10⁹⁴(95-digit number)
74825465774604281548…31237728982173310721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.496 × 10⁹⁵(96-digit number)
14965093154920856309…62475457964346621441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.993 × 10⁹⁵(96-digit number)
29930186309841712619…24950915928693242881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.986 × 10⁹⁵(96-digit number)
59860372619683425238…49901831857386485761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.197 × 10⁹⁶(97-digit number)
11972074523936685047…99803663714772971521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.394 × 10⁹⁶(97-digit number)
23944149047873370095…99607327429545943041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.788 × 10⁹⁶(97-digit number)
47888298095746740191…99214654859091886081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.577 × 10⁹⁶(97-digit number)
95776596191493480382…98429309718183772161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.915 × 10⁹⁷(98-digit number)
19155319238298696076…96858619436367544321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
3.831 × 10⁹⁷(98-digit number)
38310638476597392152…93717238872735088641
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,914,663 XPM·at block #6,833,804 · updates every 60s
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