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Block #2,009,295

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/5/2017, 9:11:12 AM Β· Difficulty 10.7010 Β· 4,833,877 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f02e034dd779af3bc685c10c5910c144e9c77dace16b317a3ebbf80652d914c2
View on Chainz β†—

Height

#2,009,295

Difficulty

10.701012

Transactions

2

Size

1.42 KB

Version

2

Bits

0ab37587

Nonce

343,991,308

Timestamp

3/5/2017, 9:11:12 AM

Confirmations

4,833,877

Mined by

⛏️ P2SHAVT4V4R3G5tgY85kfcy3uSt1FV21GEPHRR

Merkle Root

676f0c23c3d543cf28dda88cbfb0b20b5656a3893b352d003400e16077fd12bc
Transactions (2)
Coinbase9729ae812fbbe4…84eeaed310e1c4
1 in β†’ 1 out8.7400 XPM109 B
AVT4V4R3…21GEPHRR
4a7a25d9edcbd7…250d60a739d890
8 in β†’ 2 out20.1116 XPM1.23 KB
AeXVQ4CL…Uj5ivHdhAMRycWoF…13hkF5ou
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.

4.707 Γ— 10⁹³(94-digit number)
47071824305757549829…36440910732002796801
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
4.707 Γ— 10⁹³(94-digit number)
47071824305757549829…36440910732002796801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.414 Γ— 10⁹³(94-digit number)
94143648611515099658…72881821464005593601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.882 Γ— 10⁹⁴(95-digit number)
18828729722303019931…45763642928011187201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.765 Γ— 10⁹⁴(95-digit number)
37657459444606039863…91527285856022374401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.531 Γ— 10⁹⁴(95-digit number)
75314918889212079726…83054571712044748801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.506 Γ— 10⁹⁡(96-digit number)
15062983777842415945…66109143424089497601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
3.012 Γ— 10⁹⁡(96-digit number)
30125967555684831890…32218286848178995201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
6.025 Γ— 10⁹⁡(96-digit number)
60251935111369663781…64436573696357990401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.205 Γ— 10⁹⁢(97-digit number)
12050387022273932756…28873147392715980801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.410 Γ— 10⁹⁢(97-digit number)
24100774044547865512…57746294785431961601
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,989,742 XPMΒ·at block #6,843,171 Β· updates every 60s
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