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Block #845,144

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/8/2014, 4:03:57 PM Β· Difficulty 10.9726 Β· 5,987,498 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
616f5ec2f4a36a36269840e8127f45de75e318f8c70cda90ef0dff4e2ddeda3e
View on Chainz β†—

Height

#845,144

Difficulty

10.972595

Transactions

2

Size

398 B

Version

2

Bits

0af8fbf9

Nonce

73,609,041

Timestamp

12/8/2014, 4:03:57 PM

Confirmations

5,987,498

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

116a5de98006560e6d1eebcca1701008dcf82cb8434a34ffa9f72aa0e5046b0d
Transactions (2)
Coinbasebde7e5b4053cb8…83c616141a71f5
1 in β†’ 1 out8.3132 XPM116 B
ANSXnLY2…Sd25TjkD
601f68586087ed…fc182e61dc8f60
1 in β†’ 1 out0.0115 XPM192 B
AdVQ8SgV…WCHaeqka
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.

2.582 Γ— 10⁹⁡(96-digit number)
25827704966884485534…98490524784813792639
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
2.582 Γ— 10⁹⁡(96-digit number)
25827704966884485534…98490524784813792639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.165 Γ— 10⁹⁡(96-digit number)
51655409933768971069…96981049569627585279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.033 Γ— 10⁹⁢(97-digit number)
10331081986753794213…93962099139255170559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.066 Γ— 10⁹⁢(97-digit number)
20662163973507588427…87924198278510341119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.132 Γ— 10⁹⁢(97-digit number)
41324327947015176855…75848396557020682239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.264 Γ— 10⁹⁢(97-digit number)
82648655894030353710…51696793114041364479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.652 Γ— 10⁹⁷(98-digit number)
16529731178806070742…03393586228082728959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.305 Γ— 10⁹⁷(98-digit number)
33059462357612141484…06787172456165457919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.611 Γ— 10⁹⁷(98-digit number)
66118924715224282968…13574344912330915839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.322 Γ— 10⁹⁸(99-digit number)
13223784943044856593…27148689824661831679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
2.644 Γ— 10⁹⁸(99-digit number)
26447569886089713187…54297379649323663359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,905,286 XPMΒ·at block #6,832,641 Β· updates every 60s
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