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Block #856,776

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/17/2014, 8:23:56 AM Β· Difficulty 10.9678 Β· 5,986,142 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7c0dd23bf9e3dac47dc3c0b7fc33b25d82ab4a92ac5abbe4867490254eeb9e7f
View on Chainz β†—

Height

#856,776

Difficulty

10.967843

Transactions

1

Size

243 B

Version

2

Bits

0af7c490

Nonce

764,603,608

Timestamp

12/17/2014, 8:23:56 AM

Confirmations

5,986,142

Mined by

⛏️ jhPrimeminerAP7y578FR2DjwxxoaSjpc6P3V38eJ8kdV3

Merkle Root

cb84daa666036ec8a3d00cfad944915c949a898a6e8d206b8c085b3b8251aa6e
Transactions (1)
Coinbasecb84daa666036e…085b3b8251aa6e
1 in β†’ 2 out8.3000 XPM152 B
AP7y578F…8eJ8kdV3ALPu3s2c…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.

5.054 Γ— 10⁹⁢(97-digit number)
50545620155256976613…59259246736194296319
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
5.054 Γ— 10⁹⁢(97-digit number)
50545620155256976613…59259246736194296319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.010 Γ— 10⁹⁷(98-digit number)
10109124031051395322…18518493472388592639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.021 Γ— 10⁹⁷(98-digit number)
20218248062102790645…37036986944777185279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.043 Γ— 10⁹⁷(98-digit number)
40436496124205581290…74073973889554370559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.087 Γ— 10⁹⁷(98-digit number)
80872992248411162581…48147947779108741119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.617 Γ— 10⁹⁸(99-digit number)
16174598449682232516…96295895558217482239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.234 Γ— 10⁹⁸(99-digit number)
32349196899364465032…92591791116434964479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.469 Γ— 10⁹⁸(99-digit number)
64698393798728930065…85183582232869928959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.293 Γ— 10⁹⁹(100-digit number)
12939678759745786013…70367164465739857919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.587 Γ— 10⁹⁹(100-digit number)
25879357519491572026…40734328931479715839
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:57,987,691 XPMΒ·at block #6,842,917 Β· updates every 60s
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