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Block #851,659

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/13/2014, 11:41:51 AM Β· Difficulty 10.9704 Β· 5,980,940 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
94059ffb4a5a6a0dd64cb57abc79d695f3a9403dc54e8e9048422e079e278b29
View on Chainz β†—

Height

#851,659

Difficulty

10.970412

Transactions

2

Size

432 B

Version

2

Bits

0af86ce8

Nonce

1,047,859,063

Timestamp

12/13/2014, 11:41:51 AM

Confirmations

5,980,940

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

95e1625313ce56aca0a96c24e9f4f180ea9b42cf7055fb70bc852c3a9ad5ab08
Transactions (2)
Coinbase66e4f82ef044ca…fb8f2e8be99aae
1 in β†’ 1 out8.3150 XPM116 B
ANSXnLY2…Sd25TjkD
717058b28a1160…e73f4e2a74eae1
1 in β†’ 2 out0.0953 XPM226 B
AbSwo4CF…DKbJzqKKAXq7SYt5…svvbfeN9
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.

1.498 Γ— 10⁹⁡(96-digit number)
14989477971000187154…38288627164439360001
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
1.498 Γ— 10⁹⁡(96-digit number)
14989477971000187154…38288627164439360001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.997 Γ— 10⁹⁡(96-digit number)
29978955942000374309…76577254328878720001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.995 Γ— 10⁹⁡(96-digit number)
59957911884000748618…53154508657757440001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.199 Γ— 10⁹⁢(97-digit number)
11991582376800149723…06309017315514880001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.398 Γ— 10⁹⁢(97-digit number)
23983164753600299447…12618034631029760001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.796 Γ— 10⁹⁢(97-digit number)
47966329507200598895…25236069262059520001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.593 Γ— 10⁹⁢(97-digit number)
95932659014401197790…50472138524119040001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.918 Γ— 10⁹⁷(98-digit number)
19186531802880239558…00944277048238080001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.837 Γ— 10⁹⁷(98-digit number)
38373063605760479116…01888554096476160001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.674 Γ— 10⁹⁷(98-digit number)
76746127211520958232…03777108192952320001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
1.534 Γ— 10⁹⁸(99-digit number)
15349225442304191646…07554216385904640001
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,904,943 XPMΒ·at block #6,832,598 Β· updates every 60s
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