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Block #413,915

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/21/2014, 1:57:33 PM Β· Difficulty 10.4149 Β· 6,411,141 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
a4df0306f41ce1a457b82981b6c19904f97fceecdde6f8a013c214dab2eacf06
View on Chainz β†—

Height

#413,915

Difficulty

10.414927

Transactions

2

Size

838 B

Version

2

Bits

0a6a38a4

Nonce

30,708

Timestamp

2/21/2014, 1:57:33 PM

Confirmations

6,411,141

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

03e16834cdf22de5becda996e09dbd6a836653998db32fa8ec7c29c20e56197b
Transactions (2)
Coinbase38c4e63bde3f81…0ac60233862270
1 in β†’ 1 out9.2100 XPM110 B
AeKNrjNj…1NEq95Ta
98efe20414c8ea…f961cec85d05c9
4 in β†’ 1 out1.4418 XPM638 B
AL6TGZ8D…rxLmNfPQ
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.

4.871 Γ— 10⁹³(94-digit number)
48717328737312390336…62318200153437391559
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
4.871 Γ— 10⁹³(94-digit number)
48717328737312390336…62318200153437391559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.743 Γ— 10⁹³(94-digit number)
97434657474624780672…24636400306874783119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.948 Γ— 10⁹⁴(95-digit number)
19486931494924956134…49272800613749566239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.897 Γ— 10⁹⁴(95-digit number)
38973862989849912268…98545601227499132479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.794 Γ— 10⁹⁴(95-digit number)
77947725979699824537…97091202454998264959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.558 Γ— 10⁹⁡(96-digit number)
15589545195939964907…94182404909996529919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.117 Γ— 10⁹⁡(96-digit number)
31179090391879929815…88364809819993059839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.235 Γ— 10⁹⁡(96-digit number)
62358180783759859630…76729619639986119679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.247 Γ— 10⁹⁢(97-digit number)
12471636156751971926…53459239279972239359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.494 Γ— 10⁹⁢(97-digit number)
24943272313503943852…06918478559944478719
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:57,844,533 XPMΒ·at block #6,825,055 Β· updates every 60s
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