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Block #387,860

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/3/2014, 10:10:08 AM Β· Difficulty 10.4156 Β· 6,450,435 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6fe4a97ac23f6dce4c5eba51362c79bb3a6e1928091f3e05203a67d25c2fd931
View on Chainz β†—

Height

#387,860

Difficulty

10.415594

Transactions

1

Size

201 B

Version

2

Bits

0a6a6459

Nonce

30,161,601

Timestamp

2/3/2014, 10:10:08 AM

Confirmations

6,450,435

Mined by

⛏️ P2SHARbkhBHngVkgNi7FHbJqyafoZwGdxaU1p6

Merkle Root

da844148d5da3e20efc650e950b45fa7833a6cdc748081394dc7508463fe28ab
Transactions (1)
Coinbaseda844148d5da3e…c7508463fe28ab
1 in β†’ 1 out9.2000 XPM110 B
ARbkhBHn…GdxaU1p6
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.

2.225 Γ— 10⁹⁢(97-digit number)
22251927969454524804…01324444746977027199
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
2.225 Γ— 10⁹⁢(97-digit number)
22251927969454524804…01324444746977027199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.450 Γ— 10⁹⁢(97-digit number)
44503855938909049609…02648889493954054399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.900 Γ— 10⁹⁢(97-digit number)
89007711877818099218…05297778987908108799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.780 Γ— 10⁹⁷(98-digit number)
17801542375563619843…10595557975816217599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.560 Γ— 10⁹⁷(98-digit number)
35603084751127239687…21191115951632435199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.120 Γ— 10⁹⁷(98-digit number)
71206169502254479374…42382231903264870399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.424 Γ— 10⁹⁸(99-digit number)
14241233900450895874…84764463806529740799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.848 Γ— 10⁹⁸(99-digit number)
28482467800901791749…69528927613059481599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.696 Γ— 10⁹⁸(99-digit number)
56964935601803583499…39057855226118963199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.139 Γ— 10⁹⁹(100-digit number)
11392987120360716699…78115710452237926399
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:57,950,635 XPMΒ·at block #6,838,294 Β· updates every 60s
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