Block #912,305

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/27/2015, 7:13:00 PM · Difficulty 10.9294 · 5,929,804 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e79f624e60cb98778f8ef6ab26722d6dc1a67125a413021fc1e1e020d7441b8f

Height

#912,305

Difficulty

10.929418

Transactions

2

Size

724 B

Version

2

Bits

0aedee53

Nonce

1,034,815,121

Timestamp

1/27/2015, 7:13:00 PM

Confirmations

5,929,804

Merkle Root

ef85bfc8f4a86c16cfd219a9f42c52bec43890ed433580b6f0f99a72e6a9d262
Transactions (2)
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.

9.281 × 10⁹⁵(96-digit number)
92816734188459376238…96526785479570687359
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
9.281 × 10⁹⁵(96-digit number)
92816734188459376238…96526785479570687359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.856 × 10⁹⁶(97-digit number)
18563346837691875247…93053570959141374719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.712 × 10⁹⁶(97-digit number)
37126693675383750495…86107141918282749439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.425 × 10⁹⁶(97-digit number)
74253387350767500990…72214283836565498879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.485 × 10⁹⁷(98-digit number)
14850677470153500198…44428567673130997759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.970 × 10⁹⁷(98-digit number)
29701354940307000396…88857135346261995519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.940 × 10⁹⁷(98-digit number)
59402709880614000792…77714270692523991039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.188 × 10⁹⁸(99-digit number)
11880541976122800158…55428541385047982079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.376 × 10⁹⁸(99-digit number)
23761083952245600316…10857082770095964159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.752 × 10⁹⁸(99-digit number)
47522167904491200633…21714165540191928319
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:57,981,260 XPM·at block #6,842,108 · updates every 60s
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