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Block #170,309

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/18/2013, 4:33:46 PM Β· Difficulty 9.8655 Β· 6,626,331 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
13ae2f0dfcb60cab10d979091fdb44d31a42ea0ee6caae485d8be51fd6fd7934
View on Chainz β†—

Height

#170,309

Difficulty

9.865520

Transactions

2

Size

540 B

Version

2

Bits

09dd92b9

Nonce

19,139

Timestamp

9/18/2013, 4:33:46 PM

Confirmations

6,626,331

Mined by

⛏️ P2SHAWRidZFidSchvmV6ijNMVnZyMRU8XWGCxi

Merkle Root

e14cc7b143ee62334fe2ab05413e22143c5f87eadce977e03f51bd9a0681c52b
Transactions (2)
Coinbaseee2f5e3679f622…f8675edcf55256
1 in β†’ 1 out10.2700 XPM109 B
AWRidZFi…U8XWGCxi
5b04f7a0a72272…3bf6e6baa1c168
2 in β†’ 1 out3.0157 XPM340 B
AMqy1Z9q…9qLErWJg
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.

4.447 Γ— 10⁹⁢(97-digit number)
44472866282235747399…36823896685642982399
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
4.447 Γ— 10⁹⁢(97-digit number)
44472866282235747399…36823896685642982399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.894 Γ— 10⁹⁢(97-digit number)
88945732564471494799…73647793371285964799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.778 Γ— 10⁹⁷(98-digit number)
17789146512894298959…47295586742571929599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.557 Γ— 10⁹⁷(98-digit number)
35578293025788597919…94591173485143859199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.115 Γ— 10⁹⁷(98-digit number)
71156586051577195839…89182346970287718399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.423 Γ— 10⁹⁸(99-digit number)
14231317210315439167…78364693940575436799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.846 Γ— 10⁹⁸(99-digit number)
28462634420630878335…56729387881150873599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.692 Γ— 10⁹⁸(99-digit number)
56925268841261756671…13458775762301747199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.138 Γ— 10⁹⁹(100-digit number)
11385053768252351334…26917551524603494399
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,617,121 XPMΒ·at block #6,796,639 Β· updates every 60s
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