Block #370,705

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/22/2014, 8:24:42 AM · Difficulty 10.4366 · 6,439,295 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9534e097929de9e262f6ff7f3b1cb89ddea193fad7b796af2972b71c1c74ff67

Height

#370,705

Difficulty

10.436609

Transactions

3

Size

986 B

Version

2

Bits

0a6fc597

Nonce

70,686

Timestamp

1/22/2014, 8:24:42 AM

Confirmations

6,439,295

Merkle Root

90106055c9a4e01210f541948897b597f358128afb5a618dab85f008ec65d729
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.

7.589 × 10¹⁰¹(102-digit number)
75891880191439946304…01540083964563077679
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
7.589 × 10¹⁰¹(102-digit number)
75891880191439946304…01540083964563077679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.517 × 10¹⁰²(103-digit number)
15178376038287989260…03080167929126155359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.035 × 10¹⁰²(103-digit number)
30356752076575978521…06160335858252310719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.071 × 10¹⁰²(103-digit number)
60713504153151957043…12320671716504621439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.214 × 10¹⁰³(104-digit number)
12142700830630391408…24641343433009242879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.428 × 10¹⁰³(104-digit number)
24285401661260782817…49282686866018485759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.857 × 10¹⁰³(104-digit number)
48570803322521565634…98565373732036971519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.714 × 10¹⁰³(104-digit number)
97141606645043131269…97130747464073943039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.942 × 10¹⁰⁴(105-digit number)
19428321329008626253…94261494928147886079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.885 × 10¹⁰⁴(105-digit number)
38856642658017252507…88522989856295772159
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:57,724,075 XPM·at block #6,809,999 · updates every 60s
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