Block #1,520,072

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/31/2016, 12:03:01 PM · Difficulty 10.5903 · 5,296,896 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
92443504acc782b5436bb9db6418be1c836b85a4d0b314244e0e95e742c2781d

Height

#1,520,072

Difficulty

10.590287

Transactions

2

Size

1.38 KB

Version

2

Bits

0a971d0a

Nonce

349,825,338

Timestamp

3/31/2016, 12:03:01 PM

Confirmations

5,296,896

Merkle Root

3038fc0ecd51754e6d1dcac32626d0e8431f717dac4922711ebb61e48f99006a
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.

1.945 × 10⁹²(93-digit number)
19452068351798643044…53088578034655381599
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
1.945 × 10⁹²(93-digit number)
19452068351798643044…53088578034655381599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.890 × 10⁹²(93-digit number)
38904136703597286089…06177156069310763199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.780 × 10⁹²(93-digit number)
77808273407194572178…12354312138621526399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.556 × 10⁹³(94-digit number)
15561654681438914435…24708624277243052799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.112 × 10⁹³(94-digit number)
31123309362877828871…49417248554486105599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.224 × 10⁹³(94-digit number)
62246618725755657742…98834497108972211199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.244 × 10⁹⁴(95-digit number)
12449323745151131548…97668994217944422399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.489 × 10⁹⁴(95-digit number)
24898647490302263096…95337988435888844799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.979 × 10⁹⁴(95-digit number)
49797294980604526193…90675976871777689599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.959 × 10⁹⁴(95-digit number)
99594589961209052387…81351953743555379199
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:57,779,781 XPM·at block #6,816,967 · updates every 60s
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