Block #2,378,996

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/14/2017, 11:25:08 AM · Difficulty 10.8789 · 4,454,922 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
101604af7596e4c9c45d8fefc0f743a318d445c4d35905e5d772c5872ce3df70

Height

#2,378,996

Difficulty

10.878874

Transactions

3

Size

1.65 KB

Version

2

Bits

0ae0fde7

Nonce

1,075,843,574

Timestamp

11/14/2017, 11:25:08 AM

Confirmations

4,454,922

Merkle Root

f98f30a8a6b3f0e163be0732a323204f802c65870df921ad226bb0d7989489ea
Transactions (3)
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.

2.321 × 10⁹⁶(97-digit number)
23214073112268829689…60161385813510314239
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
2.321 × 10⁹⁶(97-digit number)
23214073112268829689…60161385813510314239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.642 × 10⁹⁶(97-digit number)
46428146224537659379…20322771627020628479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.285 × 10⁹⁶(97-digit number)
92856292449075318758…40645543254041256959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.857 × 10⁹⁷(98-digit number)
18571258489815063751…81291086508082513919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.714 × 10⁹⁷(98-digit number)
37142516979630127503…62582173016165027839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.428 × 10⁹⁷(98-digit number)
74285033959260255006…25164346032330055679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.485 × 10⁹⁸(99-digit number)
14857006791852051001…50328692064660111359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.971 × 10⁹⁸(99-digit number)
29714013583704102002…00657384129320222719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.942 × 10⁹⁸(99-digit number)
59428027167408204005…01314768258640445439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.188 × 10⁹⁹(100-digit number)
11885605433481640801…02629536517280890879
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,915,570 XPM·at block #6,833,917 · updates every 60s
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