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Home/Chain Registry/Block #2,054,334

Block #2,054,334

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 4/4/2017, 10:35:03 AM Β· Difficulty 10.7915 Β· 4,791,361 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
96e32573993927f325d6265eed3b8bf2de1dc38a43575e9de5f17c2c721b980c
View on Chainz β†—

Difficulty

10.791535

Transactions

1

Size

200 B

Version

2

Bits

0acaa211

Nonce

1,101,999,959

Timestamp

4/4/2017, 10:35:03 AM

Confirmations

4,791,361

Merkle Root

51375bbd57172d73450d8a7476db751497dfe767f6960a4087f74e0bfb3d824d
Transactions (1)
Coinbase51375bbd57172d…f74e0bfb3d824d
1 in β†’ 1 out8.5700 XPM110 B
AGEk9G9A…mWrSr4gf
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.

3.782 Γ— 10⁹⁡(96-digit number)
37829564173626532480…56559468443144302080
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
3.782 Γ— 10⁹⁡(96-digit number)
37829564173626532480…56559468443144302081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
7.565 Γ— 10⁹⁡(96-digit number)
75659128347253064960…13118936886288604161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.513 Γ— 10⁹⁢(97-digit number)
15131825669450612992…26237873772577208321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.026 Γ— 10⁹⁢(97-digit number)
30263651338901225984…52475747545154416641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
6.052 Γ— 10⁹⁢(97-digit number)
60527302677802451968…04951495090308833281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.210 Γ— 10⁹⁷(98-digit number)
12105460535560490393…09902990180617666561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.421 Γ— 10⁹⁷(98-digit number)
24210921071120980787…19805980361235333121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
4.842 Γ— 10⁹⁷(98-digit number)
48421842142241961574…39611960722470666241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
9.684 Γ— 10⁹⁷(98-digit number)
96843684284483923149…79223921444941332481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.936 Γ— 10⁹⁸(99-digit number)
19368736856896784629…58447842889882664961
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 2054334

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 96e32573993927f325d6265eed3b8bf2de1dc38a43575e9de5f17c2c721b980c

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 #2,054,334 on Chainz β†—
Circulating Supply:58,010,017 XPMΒ·at block #6,845,694 Β· updates every 60s
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