Block #3,242,524

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 6/27/2019, 1:25:49 AM · Difficulty 11.0012 · 3,591,429 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
95933129e5914df8540cbcb3575f949669c5a3c764dc310dcbdd47d6397ae0ca

Height

#3,242,524

Difficulty

11.001154

Transactions

5

Size

5.66 KB

Version

2

Bits

0b004ba2

Nonce

191,762,311

Timestamp

6/27/2019, 1:25:49 AM

Confirmations

3,591,429

Merkle Root

c60f61deee4a3982c15a1af6e84fcac8a50f56e1b80ce76e8d1953a774259da6
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.

8.072 × 10⁹³(94-digit number)
80722704160893533405…96179914192537379301
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
8.072 × 10⁹³(94-digit number)
80722704160893533405…96179914192537379301
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.614 × 10⁹⁴(95-digit number)
16144540832178706681…92359828385074758601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.228 × 10⁹⁴(95-digit number)
32289081664357413362…84719656770149517201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.457 × 10⁹⁴(95-digit number)
64578163328714826724…69439313540299034401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.291 × 10⁹⁵(96-digit number)
12915632665742965344…38878627080598068801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.583 × 10⁹⁵(96-digit number)
25831265331485930689…77757254161196137601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.166 × 10⁹⁵(96-digit number)
51662530662971861379…55514508322392275201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.033 × 10⁹⁶(97-digit number)
10332506132594372275…11029016644784550401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.066 × 10⁹⁶(97-digit number)
20665012265188744551…22058033289569100801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.133 × 10⁹⁶(97-digit number)
41330024530377489103…44116066579138201601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
8.266 × 10⁹⁶(97-digit number)
82660049060754978206…88232133158276403201
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:57,915,853 XPM·at block #6,833,952 · updates every 60s
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