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Block #2,036,525

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/24/2017, 1:40:17 PM Β· Difficulty 10.6781 Β· 4,772,035 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3b564b471258cc08515af01ee187a036c8ea5cd3aacdf20808d261c58f75c007
View on Chainz β†—

Height

#2,036,525

Difficulty

10.678149

Transactions

2

Size

1.54 KB

Version

2

Bits

0aad9b29

Nonce

244,908,080

Timestamp

3/24/2017, 1:40:17 PM

Confirmations

4,772,035

Mined by

⛏️ P2SHAaX6GDphdaERmCQykwQ5vjmb1XJENqoNxe

Merkle Root

553a07bd6a4e085c4b8c05b731672d160dd1b6f9320a570f72f0c2d21319ad77
Transactions (2)
Coinbase3b4b0de46167a8…1e04dd8640ec76
1 in β†’ 1 out8.7800 XPM109 B
AaX6GDph…JENqoNxe
9addb4433558dd…48bbbe8d826593
9 in β†’ 1 out407.4655 XPM1.34 KB
AJT5ZDj4…DtnSSE5g
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.388 Γ— 10⁹⁴(95-digit number)
13886726278334831833…65832929380726380639
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.388 Γ— 10⁹⁴(95-digit number)
13886726278334831833…65832929380726380639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.777 Γ— 10⁹⁴(95-digit number)
27773452556669663667…31665858761452761279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.554 Γ— 10⁹⁴(95-digit number)
55546905113339327335…63331717522905522559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.110 Γ— 10⁹⁡(96-digit number)
11109381022667865467…26663435045811045119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.221 Γ— 10⁹⁡(96-digit number)
22218762045335730934…53326870091622090239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.443 Γ— 10⁹⁡(96-digit number)
44437524090671461868…06653740183244180479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.887 Γ— 10⁹⁡(96-digit number)
88875048181342923736…13307480366488360959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.777 Γ— 10⁹⁢(97-digit number)
17775009636268584747…26614960732976721919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.555 Γ— 10⁹⁢(97-digit number)
35550019272537169494…53229921465953443839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.110 Γ— 10⁹⁢(97-digit number)
71100038545074338989…06459842931906887679
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,712,538 XPMΒ·at block #6,808,559 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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