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Block #2,271,730

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/28/2017, 10:29:23 AM Β· Difficulty 10.9540 Β· 4,554,894 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
833037a078eec62c7dcee10b33a95a16430ab278de0d33f3683938626aeb5a49
View on Chainz β†—

Height

#2,271,730

Difficulty

10.953978

Transactions

2

Size

872 B

Version

2

Bits

0af437ea

Nonce

1,030,860,665

Timestamp

8/28/2017, 10:29:23 AM

Confirmations

4,554,894

Mined by

⛏️ P2SHAdFAsZv3afW3knVT3fMh5Stt5XGsE5N6az

Merkle Root

849a38c58260fbbfb8787f7bdaac3fae271a99803a83493f351768d32978f577
Transactions (2)
Coinbasefad1ff0baaa443…7471670aaaa2f3
1 in β†’ 1 out8.3300 XPM110 B
AdFAsZv3…GsE5N6az
4255dcb468d1a7…9f9ef90eb613f4
4 in β†’ 2 out2027.5499 XPM671 B
AZa3SbHz…S8Z5GonMARaNCeSx…b8M3uhxY
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.

3.510 Γ— 10⁹⁷(98-digit number)
35101577533453914502…01830771427645870079
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
3.510 Γ— 10⁹⁷(98-digit number)
35101577533453914502…01830771427645870079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.020 Γ— 10⁹⁷(98-digit number)
70203155066907829005…03661542855291740159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.404 Γ— 10⁹⁸(99-digit number)
14040631013381565801…07323085710583480319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.808 Γ— 10⁹⁸(99-digit number)
28081262026763131602…14646171421166960639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.616 Γ— 10⁹⁸(99-digit number)
56162524053526263204…29292342842333921279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.123 Γ— 10⁹⁹(100-digit number)
11232504810705252640…58584685684667842559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.246 Γ— 10⁹⁹(100-digit number)
22465009621410505281…17169371369335685119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.493 Γ— 10⁹⁹(100-digit number)
44930019242821010563…34338742738671370239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
8.986 Γ— 10⁹⁹(100-digit number)
89860038485642021127…68677485477342740479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.797 Γ— 10¹⁰⁰(101-digit number)
17972007697128404225…37354970954685480959
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:57,857,146 XPMΒ·at block #6,826,623 Β· updates every 60s
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