Block #392,798

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/6/2014, 4:46:31 PM · Difficulty 10.4420 · 6,417,977 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
37e12767a37cd768b71f7b06be0d07a43ad6147c3b4bdd201257d2b9ca655a4e

Height

#392,798

Difficulty

10.442048

Transactions

1

Size

973 B

Version

2

Bits

0a712a0c

Nonce

54,652

Timestamp

2/6/2014, 4:46:31 PM

Confirmations

6,417,977

Merkle Root

fbcdbff2550b69409bbca64e747e2d1360b31fd1646425345ba7eabd820b9fbe
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.

3.497 × 10¹⁰³(104-digit number)
34972642735373703083…60949128770192865279
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
3.497 × 10¹⁰³(104-digit number)
34972642735373703083…60949128770192865279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
6.994 × 10¹⁰³(104-digit number)
69945285470747406167…21898257540385730559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.398 × 10¹⁰⁴(105-digit number)
13989057094149481233…43796515080771461119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.797 × 10¹⁰⁴(105-digit number)
27978114188298962466…87593030161542922239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.595 × 10¹⁰⁴(105-digit number)
55956228376597924933…75186060323085844479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.119 × 10¹⁰⁵(106-digit number)
11191245675319584986…50372120646171688959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.238 × 10¹⁰⁵(106-digit number)
22382491350639169973…00744241292343377919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.476 × 10¹⁰⁵(106-digit number)
44764982701278339946…01488482584686755839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
8.952 × 10¹⁰⁵(106-digit number)
89529965402556679893…02976965169373511679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.790 × 10¹⁰⁶(107-digit number)
17905993080511335978…05953930338747023359
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:57,730,296 XPM·at block #6,810,774 · updates every 60s
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