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Block #186,225

1CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 9/29/2013, 7:12:13 PM Β· Difficulty 9.8646 Β· 6,617,506 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
959ce2a53baee2849477eae264fe59d3c891aad6f6b4eeaf07bac0a667905110
View on Chainz β†—

Height

#186,225

Difficulty

9.864648

Transactions

1

Size

207 B

Version

2

Bits

09dd598c

Nonce

50,331,988

Timestamp

9/29/2013, 7:12:13 PM

Confirmations

6,617,506

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

0411d005b4fe3f962c37d9b3d4b227972b91a1e7fdbd3c42082113a94d0be37d
Transactions (1)
Coinbase0411d005b4fe3f…2113a94d0be37d
1 in β†’ 1 out10.2600 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.637 Γ— 10⁹⁷(98-digit number)
26376687488129019126…88883088535691321599
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
2.637 Γ— 10⁹⁷(98-digit number)
26376687488129019126…88883088535691321599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.275 Γ— 10⁹⁷(98-digit number)
52753374976258038253…77766177071382643199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.055 Γ— 10⁹⁸(99-digit number)
10550674995251607650…55532354142765286399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.110 Γ— 10⁹⁸(99-digit number)
21101349990503215301…11064708285530572799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.220 Γ— 10⁹⁸(99-digit number)
42202699981006430603…22129416571061145599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.440 Γ— 10⁹⁸(99-digit number)
84405399962012861206…44258833142122291199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.688 Γ— 10⁹⁹(100-digit number)
16881079992402572241…88517666284244582399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.376 Γ— 10⁹⁹(100-digit number)
33762159984805144482…77035332568489164799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.752 Γ— 10⁹⁹(100-digit number)
67524319969610288964…54070665136978329599
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:57,673,883 XPMΒ·at block #6,803,730 Β· updates every 60s
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