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Home/Chain Registry/Block #2,073,594

Block #2,073,594

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/16/2017, 10:31:42 PM Β· Difficulty 10.8384 Β· 4,757,527 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
6e040a5c094a00140fcc33888ba1996055b7c0025deaeafd82b3d7ae0b6c720d
View on Chainz β†—

Difficulty

10.838449

Transactions

1

Size

200 B

Version

2

Bits

0ad6a491

Nonce

130,174,090

Timestamp

4/16/2017, 10:31:42 PM

Confirmations

4,757,527

Merkle Root

c6fee425768e4e890c2e2d35e7e974bc57e7cf424ee6caa0be02cf3e5cd36285
Transactions (1)
Coinbasec6fee425768e4e…02cf3e5cd36285
1 in β†’ 1 out8.5000 XPM110 B
AVdKbHop…7MPumifQ
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.

2.709 Γ— 10⁹⁡(96-digit number)
27092401249168419429…55958519739897815520
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
2.709 Γ— 10⁹⁡(96-digit number)
27092401249168419429…55958519739897815521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.418 Γ— 10⁹⁡(96-digit number)
54184802498336838858…11917039479795631041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.083 Γ— 10⁹⁢(97-digit number)
10836960499667367771…23834078959591262081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.167 Γ— 10⁹⁢(97-digit number)
21673920999334735543…47668157919182524161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.334 Γ— 10⁹⁢(97-digit number)
43347841998669471086…95336315838365048321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.669 Γ— 10⁹⁢(97-digit number)
86695683997338942173…90672631676730096641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.733 Γ— 10⁹⁷(98-digit number)
17339136799467788434…81345263353460193281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.467 Γ— 10⁹⁷(98-digit number)
34678273598935576869…62690526706920386561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.935 Γ— 10⁹⁷(98-digit number)
69356547197871153738…25381053413840773121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.387 Γ— 10⁹⁸(99-digit number)
13871309439574230747…50762106827681546241
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 2073594

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 6e040a5c094a00140fcc33888ba1996055b7c0025deaeafd82b3d7ae0b6c720d

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 #2,073,594 on Chainz β†—
Circulating Supply:57,893,114 XPMΒ·at block #6,831,120 Β· updates every 60s
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