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Block #540,322

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/13/2014, 2:08:12 AM Β· Difficulty 10.9331 Β· 6,255,963 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e46dabf2635997b45083b607e83a45aa0a6ee228b460d175b7dac58a6f0c3e3c
View on Chainz β†—

Height

#540,322

Difficulty

10.933086

Transactions

2

Size

429 B

Version

2

Bits

0aeedebf

Nonce

180,654,248

Timestamp

5/13/2014, 2:08:12 AM

Confirmations

6,255,963

Mined by

⛏️ P2SHAaRmmLt4LMceN65kDYrhxjXuV4APLknuK2

Merkle Root

bdffe56bc7c7c85a3148d8c324d283831a9d8f932dc76189f322383cd280c68b
Transactions (2)
Coinbase3b3b3263b45db4…551497e916468c
1 in β†’ 1 out8.3600 XPM110 B
AaRmmLt4…APLknuK2
b39316ce6cc605…4c8be5d6a1dce6
1 in β†’ 2 out2.3015 XPM227 B
AbHpQaD4…Giwt7ntRAJpFqrS3…Q74rk5S7
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.

1.864 Γ— 10⁹⁸(99-digit number)
18644848641477942694…75222124386128409599
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
1.864 Γ— 10⁹⁸(99-digit number)
18644848641477942694…75222124386128409599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.728 Γ— 10⁹⁸(99-digit number)
37289697282955885388…50444248772256819199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
7.457 Γ— 10⁹⁸(99-digit number)
74579394565911770777…00888497544513638399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.491 Γ— 10⁹⁹(100-digit number)
14915878913182354155…01776995089027276799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.983 Γ— 10⁹⁹(100-digit number)
29831757826364708310…03553990178054553599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.966 Γ— 10⁹⁹(100-digit number)
59663515652729416621…07107980356109107199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.193 Γ— 10¹⁰⁰(101-digit number)
11932703130545883324…14215960712218214399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.386 Γ— 10¹⁰⁰(101-digit number)
23865406261091766648…28431921424436428799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.773 Γ— 10¹⁰⁰(101-digit number)
47730812522183533297…56863842848872857599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
9.546 Γ— 10¹⁰⁰(101-digit number)
95461625044367066594…13727685697745715199
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:57,614,283 XPMΒ·at block #6,796,284 Β· updates every 60s
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