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Block #473,811

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/4/2014, 4:27:18 AM Β· Difficulty 10.4453 Β· 6,338,481 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cf25a7bfc0a25a4afb37f702ffac91163c4d1a4859b418e6c6781bcb0a209a7e
View on Chainz β†—

Height

#473,811

Difficulty

10.445256

Transactions

1

Size

207 B

Version

2

Bits

0a71fc51

Nonce

16,781,222

Timestamp

4/4/2014, 4:27:18 AM

Confirmations

6,338,481

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

d5aab44c85cca4ef185ee70c8b68fdac8b294118b15db66603af633e692b7b0b
Transactions (1)
Coinbased5aab44c85cca4…af633e692b7b0b
1 in β†’ 1 out9.1500 XPM116 B
AbwWkWZt…kawDhufa
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.

3.069 Γ— 10⁹⁢(97-digit number)
30696573762237725149…05158852796925120639
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
3.069 Γ— 10⁹⁢(97-digit number)
30696573762237725149…05158852796925120639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.139 Γ— 10⁹⁢(97-digit number)
61393147524475450299…10317705593850241279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.227 Γ— 10⁹⁷(98-digit number)
12278629504895090059…20635411187700482559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.455 Γ— 10⁹⁷(98-digit number)
24557259009790180119…41270822375400965119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.911 Γ— 10⁹⁷(98-digit number)
49114518019580360239…82541644750801930239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.822 Γ— 10⁹⁷(98-digit number)
98229036039160720479…65083289501603860479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.964 Γ— 10⁹⁸(99-digit number)
19645807207832144095…30166579003207720959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.929 Γ— 10⁹⁸(99-digit number)
39291614415664288191…60333158006415441919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.858 Γ— 10⁹⁸(99-digit number)
78583228831328576383…20666316012830883839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.571 Γ— 10⁹⁹(100-digit number)
15716645766265715276…41332632025661767679
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:57,742,355 XPMΒ·at block #6,812,291 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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