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Block #2,457,125

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/4/2018, 10:48:05 AM Β· Difficulty 10.9539 Β· 4,385,305 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
354e4f83fb9bb9ecdf2fd3b09a4138e748336ec01cbedc36a3bb571b6823713a
View on Chainz β†—

Height

#2,457,125

Difficulty

10.953879

Transactions

1

Size

200 B

Version

2

Bits

0af43162

Nonce

965,059,224

Timestamp

1/4/2018, 10:48:05 AM

Confirmations

4,385,305

Mined by

⛏️ P2SHAPAibsUH6hnwLqCQDNJfGk7nKvPBQxRcfZ

Merkle Root

a7aadae7d421fb63ae6c224e9517a3dbb55d60a9b31da18434af5ca0012a28c8
Transactions (1)
Coinbasea7aadae7d421fb…af5ca0012a28c8
1 in β†’ 1 out8.3200 XPM110 B
APAibsUH…PBQxRcfZ
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.

4.345 Γ— 10⁹⁡(96-digit number)
43450342070228520048…38327844043101965759
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
4.345 Γ— 10⁹⁡(96-digit number)
43450342070228520048…38327844043101965759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.690 Γ— 10⁹⁡(96-digit number)
86900684140457040097…76655688086203931519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.738 Γ— 10⁹⁢(97-digit number)
17380136828091408019…53311376172407863039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.476 Γ— 10⁹⁢(97-digit number)
34760273656182816038…06622752344815726079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
6.952 Γ— 10⁹⁢(97-digit number)
69520547312365632077…13245504689631452159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.390 Γ— 10⁹⁷(98-digit number)
13904109462473126415…26491009379262904319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.780 Γ— 10⁹⁷(98-digit number)
27808218924946252831…52982018758525808639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.561 Γ— 10⁹⁷(98-digit number)
55616437849892505662…05964037517051617279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.112 Γ— 10⁹⁸(99-digit number)
11123287569978501132…11928075034103234559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.224 Γ— 10⁹⁸(99-digit number)
22246575139957002264…23856150068206469119
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:57,983,855 XPMΒ·at block #6,842,429 Β· updates every 60s
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