Block #2,923,669

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/15/2018, 6:37:24 AM · Difficulty 11.3617 · 3,917,422 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c779868beeb6bb22762d38673e2012dd7877c623eb244862dcfcb631df036ae9

Height

#2,923,669

Difficulty

11.361678

Transactions

3

Size

812 B

Version

2

Bits

0b5c96f5

Nonce

1,884,733,845

Timestamp

11/15/2018, 6:37:24 AM

Confirmations

3,917,422

Merkle Root

ed3f6816cbdf3523948e8811b0540833d7a6be875db300baa599d4593b3738e0
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.

1.028 × 10⁹⁸(99-digit number)
10282970993272984210…94554177257753845759
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
1.028 × 10⁹⁸(99-digit number)
10282970993272984210…94554177257753845759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.056 × 10⁹⁸(99-digit number)
20565941986545968420…89108354515507691519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.113 × 10⁹⁸(99-digit number)
41131883973091936841…78216709031015383039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.226 × 10⁹⁸(99-digit number)
82263767946183873683…56433418062030766079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.645 × 10⁹⁹(100-digit number)
16452753589236774736…12866836124061532159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.290 × 10⁹⁹(100-digit number)
32905507178473549473…25733672248123064319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.581 × 10⁹⁹(100-digit number)
65811014356947098946…51467344496246128639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.316 × 10¹⁰⁰(101-digit number)
13162202871389419789…02934688992492257279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.632 × 10¹⁰⁰(101-digit number)
26324405742778839578…05869377984984514559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.264 × 10¹⁰⁰(101-digit number)
52648811485557679157…11738755969969029119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.052 × 10¹⁰¹(102-digit number)
10529762297111535831…23477511939938058239
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,973,092 XPM·at block #6,841,090 · updates every 60s
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