Block #1,462,951

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/18/2016, 2:05:14 PM · Difficulty 10.7829 · 5,379,430 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
22d482656869732268e7a9c50dd495e3bec6b6b4826eb7f9d99753841ae9876b

Height

#1,462,951

Difficulty

10.782925

Transactions

2

Size

1.21 KB

Version

2

Bits

0ac86dcb

Nonce

1,509,847,491

Timestamp

2/18/2016, 2:05:14 PM

Confirmations

5,379,430

Merkle Root

e9a8629f9c8df0a929bdaf377cfc109dd0ecc1c9ac2cba468001b6a0a1cfac76
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.

8.500 × 10⁹⁵(96-digit number)
85000956629497162497…95696573772027781119
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
8.500 × 10⁹⁵(96-digit number)
85000956629497162497…95696573772027781119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.700 × 10⁹⁶(97-digit number)
17000191325899432499…91393147544055562239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.400 × 10⁹⁶(97-digit number)
34000382651798864998…82786295088111124479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.800 × 10⁹⁶(97-digit number)
68000765303597729997…65572590176222248959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.360 × 10⁹⁷(98-digit number)
13600153060719545999…31145180352444497919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.720 × 10⁹⁷(98-digit number)
27200306121439091999…62290360704888995839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.440 × 10⁹⁷(98-digit number)
54400612242878183998…24580721409777991679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.088 × 10⁹⁸(99-digit number)
10880122448575636799…49161442819555983359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.176 × 10⁹⁸(99-digit number)
21760244897151273599…98322885639111966719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.352 × 10⁹⁸(99-digit number)
43520489794302547198…96645771278223933439
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:57,983,456 XPM·at block #6,842,380 · updates every 60s
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