Block #2,550,932

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 3/5/2018, 11:13:00 PM · Difficulty 10.9892 · 4,287,155 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
3f3a2fba800fb3770b3d0fb07f49257433552e2823994edd394057bd4cb28fc4

Height

#2,550,932

Difficulty

10.989241

Transactions

2

Size

427 B

Version

2

Bits

0afd3ee7

Nonce

81,255,715

Timestamp

3/5/2018, 11:13:00 PM

Confirmations

4,287,155

Merkle Root

102538754391dfefe4e5cdc689b60d6df4281e06200be44f06b2640f7c539217
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.

1.393 × 10⁹⁶(97-digit number)
13934084164833994671…91524937425397022721
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
1.393 × 10⁹⁶(97-digit number)
13934084164833994671…91524937425397022721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.786 × 10⁹⁶(97-digit number)
27868168329667989342…83049874850794045441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.573 × 10⁹⁶(97-digit number)
55736336659335978684…66099749701588090881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.114 × 10⁹⁷(98-digit number)
11147267331867195736…32199499403176181761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.229 × 10⁹⁷(98-digit number)
22294534663734391473…64398998806352363521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.458 × 10⁹⁷(98-digit number)
44589069327468782947…28797997612704727041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.917 × 10⁹⁷(98-digit number)
89178138654937565895…57595995225409454081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.783 × 10⁹⁸(99-digit number)
17835627730987513179…15191990450818908161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.567 × 10⁹⁸(99-digit number)
35671255461975026358…30383980901637816321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
7.134 × 10⁹⁸(99-digit number)
71342510923950052716…60767961803275632641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.426 × 10⁹⁹(100-digit number)
14268502184790010543…21535923606551265281
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:57,949,046 XPM·at block #6,838,086 · updates every 60s
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