Block #1,407,228

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/10/2016, 11:04:10 AM · Difficulty 10.8063 · 5,399,686 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
52a02505bec28ef52250345fb1382b6c7852432e847bd09e7c47ab7e95b8daf8

Height

#1,407,228

Difficulty

10.806255

Transactions

2

Size

7.72 KB

Version

2

Bits

0ace66b4

Nonce

359,986,990

Timestamp

1/10/2016, 11:04:10 AM

Confirmations

5,399,686

Merkle Root

e770e3497b58dd7b73262e4e0f74be085889980208189c699e3b8ce3fac46144
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.

2.506 × 10⁹⁶(97-digit number)
25069128253078930125…37257716698375400959
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
2.506 × 10⁹⁶(97-digit number)
25069128253078930125…37257716698375400959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.013 × 10⁹⁶(97-digit number)
50138256506157860250…74515433396750801919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.002 × 10⁹⁷(98-digit number)
10027651301231572050…49030866793501603839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.005 × 10⁹⁷(98-digit number)
20055302602463144100…98061733587003207679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.011 × 10⁹⁷(98-digit number)
40110605204926288200…96123467174006415359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.022 × 10⁹⁷(98-digit number)
80221210409852576401…92246934348012830719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.604 × 10⁹⁸(99-digit number)
16044242081970515280…84493868696025661439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.208 × 10⁹⁸(99-digit number)
32088484163941030560…68987737392051322879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.417 × 10⁹⁸(99-digit number)
64176968327882061120…37975474784102645759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.283 × 10⁹⁹(100-digit number)
12835393665576412224…75950949568205291519
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:57,699,416 XPM·at block #6,806,913 · updates every 60s
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