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Block #295,578

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2013, 12:46:02 PM Β· Difficulty 9.9914 Β· 6,531,260 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5736a55a9b2eff5993d21e07ce4ea38ba9d8be7d0fe34b73505974f1fb4f3506
View on Chainz β†—

Height

#295,578

Difficulty

9.991426

Transactions

1

Size

206 B

Version

2

Bits

09fdce12

Nonce

392,966

Timestamp

12/5/2013, 12:46:02 PM

Confirmations

6,531,260

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

f26ccf8464bc3ee2cda108527c8283b171958bc55dadaf8cbde9af60e00ac6df
Transactions (1)
Coinbasef26ccf8464bc3e…e9af60e00ac6df
1 in β†’ 1 out10.0000 XPM116 B
AcLBm5Z9…S683d7c3
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.

5.379 Γ— 10⁹³(94-digit number)
53795511282422824901…84462387785457651199
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
5.379 Γ— 10⁹³(94-digit number)
53795511282422824901…84462387785457651199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.075 Γ— 10⁹⁴(95-digit number)
10759102256484564980…68924775570915302399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.151 Γ— 10⁹⁴(95-digit number)
21518204512969129960…37849551141830604799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.303 Γ— 10⁹⁴(95-digit number)
43036409025938259921…75699102283661209599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.607 Γ— 10⁹⁴(95-digit number)
86072818051876519842…51398204567322419199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.721 Γ— 10⁹⁡(96-digit number)
17214563610375303968…02796409134644838399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.442 Γ— 10⁹⁡(96-digit number)
34429127220750607937…05592818269289676799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.885 Γ— 10⁹⁡(96-digit number)
68858254441501215874…11185636538579353599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.377 Γ— 10⁹⁢(97-digit number)
13771650888300243174…22371273077158707199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.754 Γ— 10⁹⁢(97-digit number)
27543301776600486349…44742546154317414399
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:57,858,871 XPMΒ·at block #6,826,837 Β· updates every 60s
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