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Block #178,505

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/24/2013, 11:06:40 AM Β· Difficulty 9.8628 Β· 6,648,415 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
837bc9737acf47abe65a4af8cbec2614da855e8dfdd73e2b9138dbe9b998350a
View on Chainz β†—

Height

#178,505

Difficulty

9.862840

Transactions

2

Size

540 B

Version

2

Bits

09dce31d

Nonce

96,886

Timestamp

9/24/2013, 11:06:40 AM

Confirmations

6,648,415

Mined by

⛏️ P2SHARL4tm8emZzvqqVhcNqH3xtnJB7MtWbB6w

Merkle Root

4bd5a8d71f4c0294a7f010e8acf641bf4e9b59c977af328a776944e01aac2f99
Transactions (2)
Coinbase91570ae06dc8b1…a17882e0179d44
1 in β†’ 1 out10.2768 XPM109 B
ARL4tm8e…7MtWbB6w
fefae4bdd70152…bbb1d88f07edcb
2 in β†’ 1 out20.8000 XPM341 B
AbC36iz9…rPhN8kHy
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.

1.892 Γ— 10⁹⁴(95-digit number)
18927840216748503166…98800696085545704959
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
1.892 Γ— 10⁹⁴(95-digit number)
18927840216748503166…98800696085545704959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.785 Γ— 10⁹⁴(95-digit number)
37855680433497006332…97601392171091409919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.571 Γ— 10⁹⁴(95-digit number)
75711360866994012664…95202784342182819839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.514 Γ— 10⁹⁡(96-digit number)
15142272173398802532…90405568684365639679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.028 Γ— 10⁹⁡(96-digit number)
30284544346797605065…80811137368731279359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.056 Γ— 10⁹⁡(96-digit number)
60569088693595210131…61622274737462558719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.211 Γ— 10⁹⁢(97-digit number)
12113817738719042026…23244549474925117439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.422 Γ— 10⁹⁢(97-digit number)
24227635477438084052…46489098949850234879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.845 Γ— 10⁹⁢(97-digit number)
48455270954876168105…92978197899700469759
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:57,859,530 XPMΒ·at block #6,826,919 Β· updates every 60s
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