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Block #146,316

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/2/2013, 10:38:00 AM Β· Difficulty 9.8473 Β· 6,663,132 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c253d4a5e1e87f083710d7d2d94bdec3ec7dbe9bb4ff9e3500c01f3f574ea15d
View on Chainz β†—

Height

#146,316

Difficulty

9.847257

Transactions

1

Size

200 B

Version

2

Bits

09d8e5d8

Nonce

27,604

Timestamp

9/2/2013, 10:38:00 AM

Confirmations

6,663,132

Mined by

⛏️ P2SHAZeU2g2L3DVc23NKBGDPLkL6PBm694WpGV

Merkle Root

145c70e9b6788b6dbe09d7820f65c9532c9519f1d3043e766673a8d6ff282ab9
Transactions (1)
Coinbase145c70e9b6788b…73a8d6ff282ab9
1 in β†’ 1 out10.3000 XPM109 B
AZeU2g2L…m694WpGV
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.

3.647 Γ— 10⁹⁢(97-digit number)
36477606308282649895…97269854611232106239
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
3.647 Γ— 10⁹⁢(97-digit number)
36477606308282649895…97269854611232106239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
7.295 Γ— 10⁹⁢(97-digit number)
72955212616565299791…94539709222464212479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.459 Γ— 10⁹⁷(98-digit number)
14591042523313059958…89079418444928424959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.918 Γ— 10⁹⁷(98-digit number)
29182085046626119916…78158836889856849919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
5.836 Γ— 10⁹⁷(98-digit number)
58364170093252239832…56317673779713699839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.167 Γ— 10⁹⁸(99-digit number)
11672834018650447966…12635347559427399679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.334 Γ— 10⁹⁸(99-digit number)
23345668037300895933…25270695118854799359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
4.669 Γ— 10⁹⁸(99-digit number)
46691336074601791866…50541390237709598719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
9.338 Γ— 10⁹⁸(99-digit number)
93382672149203583732…01082780475419197439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.867 Γ— 10⁹⁹(100-digit number)
18676534429840716746…02165560950838394879
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:57,719,655 XPMΒ·at block #6,809,447 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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