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Block #546,923

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/16/2014, 4:02:43 AM Β· Difficulty 10.9567 Β· 6,262,014 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
62daf9b30a06a25f36d9f086b5471458209b70d417059f2e79818af88267364e
View on Chainz β†—

Height

#546,923

Difficulty

10.956669

Transactions

1

Size

243 B

Version

2

Bits

0af4e83b

Nonce

354,845,627

Timestamp

5/16/2014, 4:02:43 AM

Confirmations

6,262,014

Mined by

⛏️ P2SHARzmpY4cAhz8WiJkMBTqRELns6fvx8bF9t

Merkle Root

d178bf30abd973ce8cf05b5b3c6ace0293211d7732320759abad1fac4e3e724e
Transactions (1)
Coinbased178bf30abd973…ad1fac4e3e724e
1 in β†’ 2 out8.3200 XPM152 B
ARzmpY4c…fvx8bF9tALPu3s2c…EJXLjVFh
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.

1.726 Γ— 10⁹⁸(99-digit number)
17265657399544092759…65744388095694612479
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
1.726 Γ— 10⁹⁸(99-digit number)
17265657399544092759…65744388095694612479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
3.453 Γ— 10⁹⁸(99-digit number)
34531314799088185519…31488776191389224959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
6.906 Γ— 10⁹⁸(99-digit number)
69062629598176371038…62977552382778449919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.381 Γ— 10⁹⁹(100-digit number)
13812525919635274207…25955104765556899839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.762 Γ— 10⁹⁹(100-digit number)
27625051839270548415…51910209531113799679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
5.525 Γ— 10⁹⁹(100-digit number)
55250103678541096830…03820419062227599359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.105 Γ— 10¹⁰⁰(101-digit number)
11050020735708219366…07640838124455198719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.210 Γ— 10¹⁰⁰(101-digit number)
22100041471416438732…15281676248910397439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
4.420 Γ— 10¹⁰⁰(101-digit number)
44200082942832877464…30563352497820794879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
8.840 Γ— 10¹⁰⁰(101-digit number)
88400165885665754928…61126704995641589759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.768 Γ— 10¹⁰¹(102-digit number)
17680033177133150985…22253409991283179519
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:57,715,553 XPMΒ·at block #6,808,936 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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