Block #3,371,485

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 9/27/2019, 1:29:31 PM · Difficulty 10.9949 · 3,433,483 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7ef9f5a0cba3c1869a8aab6c1ac38445ac2a4b7cdc5b042bf508f394aee5a325

Height

#3,371,485

Difficulty

10.994902

Transactions

5

Size

1.75 KB

Version

2

Bits

0afeb1e5

Nonce

2,128,791,492

Timestamp

9/27/2019, 1:29:31 PM

Confirmations

3,433,483

Merkle Root

6fc74ff5c0cc7e4532b00835dfbb53a76c1aa09099299fdf34baa4b6f86d99b0
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.

1.447 × 10⁹⁵(96-digit number)
14476203300138230581…13606408516002906879
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
1.447 × 10⁹⁵(96-digit number)
14476203300138230581…13606408516002906879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.895 × 10⁹⁵(96-digit number)
28952406600276461163…27212817032005813759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.790 × 10⁹⁵(96-digit number)
57904813200552922327…54425634064011627519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.158 × 10⁹⁶(97-digit number)
11580962640110584465…08851268128023255039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.316 × 10⁹⁶(97-digit number)
23161925280221168930…17702536256046510079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.632 × 10⁹⁶(97-digit number)
46323850560442337861…35405072512093020159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.264 × 10⁹⁶(97-digit number)
92647701120884675723…70810145024186040319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.852 × 10⁹⁷(98-digit number)
18529540224176935144…41620290048372080639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.705 × 10⁹⁷(98-digit number)
37059080448353870289…83240580096744161279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.411 × 10⁹⁷(98-digit number)
74118160896707740578…66481160193488322559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.482 × 10⁹⁸(99-digit number)
14823632179341548115…32962320386976645119
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:57,683,812 XPM·at block #6,804,967 · updates every 60s
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