Block #2,924,815

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/16/2018, 2:17:23 AM · Difficulty 11.3573 · 3,913,980 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
66f488e4abfe0ebc24832e70c62dd22c95ce0611ff0d77d52336b92e229ec719

Height

#2,924,815

Difficulty

11.357276

Transactions

29

Size

9.37 KB

Version

2

Bits

0b5b7673

Nonce

525,058,381

Timestamp

11/16/2018, 2:17:23 AM

Confirmations

3,913,980

Merkle Root

9ae7e0b8295d328203fd45cc40192497371ff0d83a909c2508e4419b5d11ee91
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.

1.143 × 10⁹⁶(97-digit number)
11437837965374117899…46437527023531371521
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
1.143 × 10⁹⁶(97-digit number)
11437837965374117899…46437527023531371521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.287 × 10⁹⁶(97-digit number)
22875675930748235799…92875054047062743041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.575 × 10⁹⁶(97-digit number)
45751351861496471598…85750108094125486081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.150 × 10⁹⁶(97-digit number)
91502703722992943197…71500216188250972161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.830 × 10⁹⁷(98-digit number)
18300540744598588639…43000432376501944321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.660 × 10⁹⁷(98-digit number)
36601081489197177279…86000864753003888641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.320 × 10⁹⁷(98-digit number)
73202162978394354558…72001729506007777281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.464 × 10⁹⁸(99-digit number)
14640432595678870911…44003459012015554561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.928 × 10⁹⁸(99-digit number)
29280865191357741823…88006918024031109121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.856 × 10⁹⁸(99-digit number)
58561730382715483646…76013836048062218241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.171 × 10⁹⁹(100-digit number)
11712346076543096729…52027672096124436481
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:57,954,623 XPM·at block #6,838,794 · updates every 60s
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