Block #914,451

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/29/2015, 9:27:17 AM · Difficulty 10.9274 · 5,895,171 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e4028bbf210423f92407cd542484b33c1acc01f33b57b06a71a725e5daff422c

Height

#914,451

Difficulty

10.927369

Transactions

11

Size

7.03 KB

Version

2

Bits

0aed6812

Nonce

103,687,780

Timestamp

1/29/2015, 9:27:17 AM

Confirmations

5,895,171

Merkle Root

95c7a288f1e66b641f23cb102c368b872209fb3453b69c71b697e6015e46eb23
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.

2.524 × 10⁹⁴(95-digit number)
25245906886460245010…98443857624895774159
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
2.524 × 10⁹⁴(95-digit number)
25245906886460245010…98443857624895774159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.049 × 10⁹⁴(95-digit number)
50491813772920490020…96887715249791548319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.009 × 10⁹⁵(96-digit number)
10098362754584098004…93775430499583096639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.019 × 10⁹⁵(96-digit number)
20196725509168196008…87550860999166193279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.039 × 10⁹⁵(96-digit number)
40393451018336392016…75101721998332386559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.078 × 10⁹⁵(96-digit number)
80786902036672784033…50203443996664773119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.615 × 10⁹⁶(97-digit number)
16157380407334556806…00406887993329546239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.231 × 10⁹⁶(97-digit number)
32314760814669113613…00813775986659092479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.462 × 10⁹⁶(97-digit number)
64629521629338227226…01627551973318184959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.292 × 10⁹⁷(98-digit number)
12925904325867645445…03255103946636369919
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:57,721,054 XPM·at block #6,809,621 · updates every 60s
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