Block #1,224,671

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/6/2015, 2:28:02 PM · Difficulty 10.7391 · 5,592,497 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9edfb407307f2aefc67f2f26ed49dcac4c5572c1b2bbea857d292c434fdc7cf0

Height

#1,224,671

Difficulty

10.739087

Transactions

2

Size

1.43 KB

Version

2

Bits

0abd34c7

Nonce

113,194,006

Timestamp

9/6/2015, 2:28:02 PM

Confirmations

5,592,497

Merkle Root

629792834e03ed79eda9089e57e629534167613c94c96e4d1f196fe80d3a7d99
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.

2.220 × 10⁹⁴(95-digit number)
22203437455846997661…62055916009019340799
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
2.220 × 10⁹⁴(95-digit number)
22203437455846997661…62055916009019340799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.440 × 10⁹⁴(95-digit number)
44406874911693995323…24111832018038681599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.881 × 10⁹⁴(95-digit number)
88813749823387990647…48223664036077363199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.776 × 10⁹⁵(96-digit number)
17762749964677598129…96447328072154726399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.552 × 10⁹⁵(96-digit number)
35525499929355196259…92894656144309452799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.105 × 10⁹⁵(96-digit number)
71050999858710392518…85789312288618905599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.421 × 10⁹⁶(97-digit number)
14210199971742078503…71578624577237811199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.842 × 10⁹⁶(97-digit number)
28420399943484157007…43157249154475622399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.684 × 10⁹⁶(97-digit number)
56840799886968314014…86314498308951244799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.136 × 10⁹⁷(98-digit number)
11368159977393662802…72628996617902489599
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:57,781,378 XPM·at block #6,817,167 · updates every 60s
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