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Block #578,253

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/5/2014, 10:06:32 PM Β· Difficulty 10.9684 Β· 6,228,056 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7d058ce96ad40d4d033c2a69733b331feb1e775a5ef8e9877975c99c676e377e
View on Chainz β†—

Height

#578,253

Difficulty

10.968358

Transactions

2

Size

845 B

Version

2

Bits

0af7e64f

Nonce

103,281,004

Timestamp

6/5/2014, 10:06:32 PM

Confirmations

6,228,056

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

019cec860cde0fb6e2076010526827236fa7391d0ec108fc72d18d541d0fd255
Transactions (2)
Coinbasea150b0d5e750a5…b7732d62f8912a
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
3f9af21608bde2…a5ca725a5c9145
4 in β†’ 1 out9.3576 XPM637 B
AMLEZ4Rp…95EAfeYV
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.

1.073 Γ— 10¹⁰⁰(101-digit number)
10739004887339985116…70286019094907699199
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
1.073 Γ— 10¹⁰⁰(101-digit number)
10739004887339985116…70286019094907699199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.147 Γ— 10¹⁰⁰(101-digit number)
21478009774679970233…40572038189815398399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.295 Γ— 10¹⁰⁰(101-digit number)
42956019549359940467…81144076379630796799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.591 Γ— 10¹⁰⁰(101-digit number)
85912039098719880934…62288152759261593599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.718 Γ— 10¹⁰¹(102-digit number)
17182407819743976186…24576305518523187199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.436 Γ— 10¹⁰¹(102-digit number)
34364815639487952373…49152611037046374399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.872 Γ— 10¹⁰¹(102-digit number)
68729631278975904747…98305222074092748799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.374 Γ— 10¹⁰²(103-digit number)
13745926255795180949…96610444148185497599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.749 Γ— 10¹⁰²(103-digit number)
27491852511590361898…93220888296370995199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.498 Γ— 10¹⁰²(103-digit number)
54983705023180723797…86441776592741990399
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:57,694,560 XPMΒ·at block #6,806,308 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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