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Block #845,912

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/9/2014, 5:22:41 AM Β· Difficulty 10.9725 Β· 5,996,855 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1ac7937348c79a68e79cdcc34948c21ebe40c2f4a300c0ce0dc0d7450551eb73
View on Chainz β†—

Height

#845,912

Difficulty

10.972460

Transactions

2

Size

433 B

Version

2

Bits

0af8f31f

Nonce

229,855,739

Timestamp

12/9/2014, 5:22:41 AM

Confirmations

5,996,855

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0d2cdd507995ab67d7264ff8fa16cec17cb45766e7c097cf42be48f4a5fd6cf2
Transactions (2)
Coinbase3b6b9daa0c15f3…09a87a8a8733b0
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
b8a4eea154ed88…0178d3b8f75483
1 in β†’ 2 out0.0925 XPM227 B
AMFuE37R…R4cggectASkBbL3G…ahbEGrwt
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.

6.882 Γ— 10⁹⁡(96-digit number)
68827583960342458318…90828739433596740239
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
6.882 Γ— 10⁹⁡(96-digit number)
68827583960342458318…90828739433596740239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.376 Γ— 10⁹⁢(97-digit number)
13765516792068491663…81657478867193480479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.753 Γ— 10⁹⁢(97-digit number)
27531033584136983327…63314957734386960959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.506 Γ— 10⁹⁢(97-digit number)
55062067168273966654…26629915468773921919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.101 Γ— 10⁹⁷(98-digit number)
11012413433654793330…53259830937547843839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.202 Γ— 10⁹⁷(98-digit number)
22024826867309586661…06519661875095687679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.404 Γ— 10⁹⁷(98-digit number)
44049653734619173323…13039323750191375359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.809 Γ— 10⁹⁷(98-digit number)
88099307469238346647…26078647500382750719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.761 Γ— 10⁹⁸(99-digit number)
17619861493847669329…52157295000765501439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.523 Γ— 10⁹⁸(99-digit number)
35239722987695338658…04314590001531002879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
7.047 Γ— 10⁹⁸(99-digit number)
70479445975390677317…08629180003062005759
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:57,986,475 XPMΒ·at block #6,842,766 Β· updates every 60s
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