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Home/Chain Registry/Block #1,507,636

Block #1,507,636

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 3/22/2016, 1:12:34 PM Β· Difficulty 10.6253 Β· 5,319,536 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6c9e353eeaaee6ffe3b86ef4a2ef51486953448be5ae124d0799d4532b55d1bc
View on Chainz β†—

Difficulty

10.625308

Transactions

2

Size

17.57 KB

Version

2

Bits

0aa01434

Nonce

68,929,478

Timestamp

3/22/2016, 1:12:34 PM

Confirmations

5,319,536

Merkle Root

cf4b7e5bd7c2486131117b5f69688b694cbd3324bcb45153cbed3d4d55b8bbf6
Transactions (2)
Coinbase1965583fd6573a…00558394dabc95
1 in β†’ 1 out9.1100 XPM109 B
AN96wRfQ…XK8fRFmE
0db3a92aa48bcd…197acfa8705cea
120 in β†’ 1 out15.0000 XPM17.38 KB
AW9z6iyE…ZMok5rfx
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.

6.451 Γ— 10⁹⁴(95-digit number)
64517419802554136314…80473412089235465280
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
6.451 Γ— 10⁹⁴(95-digit number)
64517419802554136314…80473412089235465281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.290 Γ— 10⁹⁡(96-digit number)
12903483960510827262…60946824178470930561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.580 Γ— 10⁹⁡(96-digit number)
25806967921021654525…21893648356941861121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.161 Γ— 10⁹⁡(96-digit number)
51613935842043309051…43787296713883722241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.032 Γ— 10⁹⁢(97-digit number)
10322787168408661810…87574593427767444481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.064 Γ— 10⁹⁢(97-digit number)
20645574336817323620…75149186855534888961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.129 Γ— 10⁹⁢(97-digit number)
41291148673634647240…50298373711069777921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
8.258 Γ— 10⁹⁢(97-digit number)
82582297347269294481…00596747422139555841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.651 Γ— 10⁹⁷(98-digit number)
16516459469453858896…01193494844279111681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.303 Γ— 10⁹⁷(98-digit number)
33032918938907717792…02386989688558223361
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.

View full Prime Chain Discovery page β†’
β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10
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, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 1507636

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 6c9e353eeaaee6ffe3b86ef4a2ef51486953448be5ae124d0799d4532b55d1bc

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #1,507,636 on Chainz β†—
Circulating Supply:57,861,472 XPMΒ·at block #6,827,171 Β· updates every 60s
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