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Block #163,487

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/14/2013, 12:50:05 AM Β· Difficulty 9.8619 Β· 6,663,398 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
778feb243df459152f2b6796772f145bba14c02d808cde58129d1956caade3a6
View on Chainz β†—

Height

#163,487

Difficulty

9.861900

Transactions

2

Size

359 B

Version

2

Bits

09dca57a

Nonce

34,729

Timestamp

9/14/2013, 12:50:05 AM

Confirmations

6,663,398

Mined by

⛏️ P2SHAYyPPXgF5A3RKbdbyWYgDSxAkdb6nr5cD2

Merkle Root

2e0a45618a4b5225a2054bd3d534db6928f9eab3567ea243176c39d05e4aabed
Transactions (2)
Coinbasebd9f505b6e43f0…9ca66c4ea91c84
1 in β†’ 1 out10.2800 XPM109 B
AYyPPXgF…b6nr5cD2
2d52941b7ac1a3…d44830be93bd2a
1 in β†’ 1 out10.2500 XPM159 B
Aa571JXD…1d4PwSHX
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.

6.218 Γ— 10⁹⁢(97-digit number)
62186034222106071341…61812858978577624319
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
6.218 Γ— 10⁹⁢(97-digit number)
62186034222106071341…61812858978577624319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.243 Γ— 10⁹⁷(98-digit number)
12437206844421214268…23625717957155248639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.487 Γ— 10⁹⁷(98-digit number)
24874413688842428536…47251435914310497279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.974 Γ— 10⁹⁷(98-digit number)
49748827377684857072…94502871828620994559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.949 Γ— 10⁹⁷(98-digit number)
99497654755369714145…89005743657241989119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.989 Γ— 10⁹⁸(99-digit number)
19899530951073942829…78011487314483978239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.979 Γ— 10⁹⁸(99-digit number)
39799061902147885658…56022974628967956479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.959 Γ— 10⁹⁸(99-digit number)
79598123804295771316…12045949257935912959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.591 Γ— 10⁹⁹(100-digit number)
15919624760859154263…24091898515871825919
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,859,245 XPMΒ·at block #6,826,884 Β· updates every 60s
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