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Block #1,479,832

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/2/2016, 6:08:41 AM Β· Difficulty 10.7162 Β· 5,362,470 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d67b742f85a83bbe0504e1588371a0af8c17bfbb9c86c6fd47b179552d0aa144
View on Chainz β†—

Height

#1,479,832

Difficulty

10.716163

Transactions

1

Size

242 B

Version

2

Bits

0ab75673

Nonce

848,209,184

Timestamp

3/2/2016, 6:08:41 AM

Confirmations

5,362,470

Mined by

⛏️ P2SHAdwKJkgSub5gUckyBUnSUJCm23L2zsc2ej

Merkle Root

1e55d39db01ea4d4e9a552168da1d6c181581c5d29c026f17aa656420b64e028
Transactions (1)
Coinbase1e55d39db01ea4…a656420b64e028
1 in β†’ 2 out8.6900 XPM152 B
AdwKJkgS…L2zsc2ejALPu3s2c…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.

9.886 Γ— 10⁹⁴(95-digit number)
98860952265404513544…67365112131948155399
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
9.886 Γ— 10⁹⁴(95-digit number)
98860952265404513544…67365112131948155399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.977 Γ— 10⁹⁡(96-digit number)
19772190453080902708…34730224263896310799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.954 Γ— 10⁹⁡(96-digit number)
39544380906161805417…69460448527792621599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.908 Γ— 10⁹⁡(96-digit number)
79088761812323610835…38920897055585243199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.581 Γ— 10⁹⁢(97-digit number)
15817752362464722167…77841794111170486399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.163 Γ— 10⁹⁢(97-digit number)
31635504724929444334…55683588222340972799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.327 Γ— 10⁹⁢(97-digit number)
63271009449858888668…11367176444681945599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.265 Γ— 10⁹⁷(98-digit number)
12654201889971777733…22734352889363891199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.530 Γ— 10⁹⁷(98-digit number)
25308403779943555467…45468705778727782399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.061 Γ— 10⁹⁷(98-digit number)
50616807559887110934…90937411557455564799
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:57,982,821 XPMΒ·at block #6,842,301 Β· updates every 60s
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