Block #2,604,954

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/8/2018, 3:51:58 AM · Difficulty 11.2994 · 4,226,071 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4841a3566bda8bf184bca3ff1e46d177f1a5fc07dc5ecaaddca49af280aab085

Height

#2,604,954

Difficulty

11.299398

Transactions

2

Size

5.89 KB

Version

2

Bits

0b4ca555

Nonce

953,911,059

Timestamp

4/8/2018, 3:51:58 AM

Confirmations

4,226,071

Merkle Root

ba7249c24a3b8a0ef1d586f7cccce0d43db32c12f28d23152126e7e017c3af65
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.

8.049 × 10⁹⁵(96-digit number)
80495356914419795760…30924834660023869441
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
8.049 × 10⁹⁵(96-digit number)
80495356914419795760…30924834660023869441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.609 × 10⁹⁶(97-digit number)
16099071382883959152…61849669320047738881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.219 × 10⁹⁶(97-digit number)
32198142765767918304…23699338640095477761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.439 × 10⁹⁶(97-digit number)
64396285531535836608…47398677280190955521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.287 × 10⁹⁷(98-digit number)
12879257106307167321…94797354560381911041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.575 × 10⁹⁷(98-digit number)
25758514212614334643…89594709120763822081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.151 × 10⁹⁷(98-digit number)
51517028425228669286…79189418241527644161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.030 × 10⁹⁸(99-digit number)
10303405685045733857…58378836483055288321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.060 × 10⁹⁸(99-digit number)
20606811370091467714…16757672966110576641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.121 × 10⁹⁸(99-digit number)
41213622740182935429…33515345932221153281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
8.242 × 10⁹⁸(99-digit number)
82427245480365870858…67030691864442306561
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:57,892,334 XPM·at block #6,831,024 · updates every 60s
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