Block #1,226,012

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/7/2015, 1:24:45 PM · Difficulty 10.7372 · 5,577,735 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2919f1527114b908be7e4fe2e6acb0d2393b82eb214c3c5e07d523858e37cf73

Height

#1,226,012

Difficulty

10.737241

Transactions

3

Size

1.07 KB

Version

2

Bits

0abcbbd4

Nonce

2,111,643,524

Timestamp

9/7/2015, 1:24:45 PM

Confirmations

5,577,735

Merkle Root

d6ed89e458549006962d875359999850c1b61959cd8d48b137160b7ae50c905b
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.

1.001 × 10⁹³(94-digit number)
10019948055928405100…01916110788562047359
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
1.001 × 10⁹³(94-digit number)
10019948055928405100…01916110788562047359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.003 × 10⁹³(94-digit number)
20039896111856810200…03832221577124094719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.007 × 10⁹³(94-digit number)
40079792223713620401…07664443154248189439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
8.015 × 10⁹³(94-digit number)
80159584447427240803…15328886308496378879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.603 × 10⁹⁴(95-digit number)
16031916889485448160…30657772616992757759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.206 × 10⁹⁴(95-digit number)
32063833778970896321…61315545233985515519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
6.412 × 10⁹⁴(95-digit number)
64127667557941792643…22631090467971031039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.282 × 10⁹⁵(96-digit number)
12825533511588358528…45262180935942062079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.565 × 10⁹⁵(96-digit number)
25651067023176717057…90524361871884124159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
5.130 × 10⁹⁵(96-digit number)
51302134046353434114…81048723743768248319
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:57,674,014 XPM·at block #6,803,746 · updates every 60s
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