Block #1,420,015

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/19/2016, 3:07:54 PM · Difficulty 10.7900 · 5,416,606 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b2dcfef52426fc9288e26777ca41c5a786dd2b7025e95fa18e4123d1141aed3f

Height

#1,420,015

Difficulty

10.790013

Transactions

2

Size

937 B

Version

2

Bits

0aca3e46

Nonce

1,152,150,952

Timestamp

1/19/2016, 3:07:54 PM

Confirmations

5,416,606

Merkle Root

620df6c4919e5121e18553fba9079fe17e462e7bef43e5367143191ce7ace8e7
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.

7.564 × 10⁹⁶(97-digit number)
75647108057476384520…79600189383016447999
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
7.564 × 10⁹⁶(97-digit number)
75647108057476384520…79600189383016447999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.512 × 10⁹⁷(98-digit number)
15129421611495276904…59200378766032895999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.025 × 10⁹⁷(98-digit number)
30258843222990553808…18400757532065791999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.051 × 10⁹⁷(98-digit number)
60517686445981107616…36801515064131583999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.210 × 10⁹⁸(99-digit number)
12103537289196221523…73603030128263167999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.420 × 10⁹⁸(99-digit number)
24207074578392443046…47206060256526335999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.841 × 10⁹⁸(99-digit number)
48414149156784886093…94412120513052671999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.682 × 10⁹⁸(99-digit number)
96828298313569772186…88824241026105343999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.936 × 10⁹⁹(100-digit number)
19365659662713954437…77648482052210687999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.873 × 10⁹⁹(100-digit number)
38731319325427908874…55296964104421375999
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:57,937,239 XPM·at block #6,836,620 · updates every 60s
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