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Block #722,811

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/15/2014, 7:05:21 PM Β· Difficulty 10.9564 Β· 6,071,920 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d690720aefa5f60bcd6d8db74880087c4e35106be503f91484a72a0c98ff16a8
View on Chainz β†—

Height

#722,811

Difficulty

10.956363

Transactions

2

Size

580 B

Version

2

Bits

0af4d434

Nonce

660,396,769

Timestamp

9/15/2014, 7:05:21 PM

Confirmations

6,071,920

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

82a4c6d6d04114ed12f9007b73aa1f4ef11ae35cc3d061e61b0bc4f5faf370f7
Transactions (2)
Coinbase6e3fdc8598c730…03b2ad03296364
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
0af239585a93a9…9b4963044d981e
2 in β†’ 2 out2.8236 XPM373 B
AeKNrjNj…1NEq95TaAWQhak32…eArVqMxc
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.

4.330 Γ— 10⁹⁷(98-digit number)
43307766141423423016…07697154092381271039
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
4.330 Γ— 10⁹⁷(98-digit number)
43307766141423423016…07697154092381271039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.661 Γ— 10⁹⁷(98-digit number)
86615532282846846032…15394308184762542079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.732 Γ— 10⁹⁸(99-digit number)
17323106456569369206…30788616369525084159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.464 Γ— 10⁹⁸(99-digit number)
34646212913138738413…61577232739050168319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.929 Γ— 10⁹⁸(99-digit number)
69292425826277476826…23154465478100336639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.385 Γ— 10⁹⁹(100-digit number)
13858485165255495365…46308930956200673279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.771 Γ— 10⁹⁹(100-digit number)
27716970330510990730…92617861912401346559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.543 Γ— 10⁹⁹(100-digit number)
55433940661021981461…85235723824802693119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.108 Γ— 10¹⁰⁰(101-digit number)
11086788132204396292…70471447649605386239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.217 Γ— 10¹⁰⁰(101-digit number)
22173576264408792584…40942895299210772479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.434 Γ— 10¹⁰⁰(101-digit number)
44347152528817585168…81885790598421544959
Verify on FactorDB β†—Wolfram Alpha β†—

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 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
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 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:57,601,898 XPMΒ·at block #6,794,730 Β· updates every 60s
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