Block #792,939

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/2/2014, 12:07:15 AM · Difficulty 10.9739 · 6,017,903 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5b9afc6eb86ac8d78be35375dcdb5c551dc315aa30ef53ba07b566a3eb3de31d

Height

#792,939

Difficulty

10.973941

Transactions

3

Size

658 B

Version

2

Bits

0af9542b

Nonce

150,928,033

Timestamp

11/2/2014, 12:07:15 AM

Confirmations

6,017,903

Merkle Root

c5628b528e094a3e0e54a0564960caef744b692342398c2659f6456ee6b67c79
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.

2.494 × 10⁹⁵(96-digit number)
24941470512561565308…33548570646901224959
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
2.494 × 10⁹⁵(96-digit number)
24941470512561565308…33548570646901224959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.988 × 10⁹⁵(96-digit number)
49882941025123130616…67097141293802449919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.976 × 10⁹⁵(96-digit number)
99765882050246261233…34194282587604899839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.995 × 10⁹⁶(97-digit number)
19953176410049252246…68388565175209799679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.990 × 10⁹⁶(97-digit number)
39906352820098504493…36777130350419599359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.981 × 10⁹⁶(97-digit number)
79812705640197008986…73554260700839198719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.596 × 10⁹⁷(98-digit number)
15962541128039401797…47108521401678397439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.192 × 10⁹⁷(98-digit number)
31925082256078803594…94217042803356794879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.385 × 10⁹⁷(98-digit number)
63850164512157607189…88434085606713589759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.277 × 10⁹⁸(99-digit number)
12770032902431521437…76868171213427179519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
2.554 × 10⁹⁸(99-digit number)
25540065804863042875…53736342426854359039
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,730,831 XPM·at block #6,810,841 · updates every 60s
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