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Block #2,482,465

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/20/2018, 11:49:59 PM Β· Difficulty 10.9666 Β· 4,361,360 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
37514057b4b4afc0c6fa2653c9253d9001b56a458c3b363f4ea18eff5941fe7d
View on Chainz β†—

Height

#2,482,465

Difficulty

10.966564

Transactions

2

Size

426 B

Version

2

Bits

0af770c4

Nonce

171,866,015

Timestamp

1/20/2018, 11:49:59 PM

Confirmations

4,361,360

Mined by

⛏️ P2SHAXiWe2ydoqyTXVrCoqaFBYGyLGTyvSHsh9

Merkle Root

27a9599be22af18610051a531cad06fd035b7e63e7708393ef213817501b0d19
Transactions (2)
Coinbase2a4b704568e782…2fbe71c379cb7b
1 in β†’ 1 out8.3100 XPM109 B
AXiWe2yd…TyvSHsh9
6373ea29e39fac…750a0e53e9d325
1 in β†’ 2 out63.1602 XPM227 B
AdDSPtwE…P3JHB2wtAXFWE8h1…6DHu8ium
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.

1.223 Γ— 10⁹⁴(95-digit number)
12232868128708233730…68081088335976248769
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
1.223 Γ— 10⁹⁴(95-digit number)
12232868128708233730…68081088335976248769
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.446 Γ— 10⁹⁴(95-digit number)
24465736257416467461…36162176671952497539
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.893 Γ— 10⁹⁴(95-digit number)
48931472514832934922…72324353343904995079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.786 Γ— 10⁹⁴(95-digit number)
97862945029665869844…44648706687809990159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.957 Γ— 10⁹⁡(96-digit number)
19572589005933173968…89297413375619980319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.914 Γ— 10⁹⁡(96-digit number)
39145178011866347937…78594826751239960639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.829 Γ— 10⁹⁡(96-digit number)
78290356023732695875…57189653502479921279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.565 Γ— 10⁹⁢(97-digit number)
15658071204746539175…14379307004959842559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.131 Γ— 10⁹⁢(97-digit number)
31316142409493078350…28758614009919685119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.263 Γ— 10⁹⁢(97-digit number)
62632284818986156700…57517228019839370239
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:57,994,975 XPMΒ·at block #6,843,824 Β· updates every 60s
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