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Home/Chain Registry/Block #2,121,524

Block #2,121,524

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/18/2017, 1:52:03 AM Β· Difficulty 10.9136 Β· 4,709,282 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d2253409ed20dd1b4db956d815f1d601ac800fd2f3ad8a0d2d03d1653ee4bcb0
View on Chainz β†—

Difficulty

10.913584

Transactions

1

Size

200 B

Version

2

Bits

0ae9e09f

Nonce

448,724,741

Timestamp

5/18/2017, 1:52:03 AM

Confirmations

4,709,282

Merkle Root

4b0ef08edbc03330ab74b6cc2a2ecce2921776aa6e709721f8a47eeb6aae3aa1
Transactions (1)
Coinbase4b0ef08edbc033…a47eeb6aae3aa1
1 in β†’ 1 out8.3800 XPM110 B
AUgA93tr…JseFqFN7
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.

7.078 Γ— 10⁹⁴(95-digit number)
70780904147952395239…45491040127455479680
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
7.078 Γ— 10⁹⁴(95-digit number)
70780904147952395239…45491040127455479681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.415 Γ— 10⁹⁡(96-digit number)
14156180829590479047…90982080254910959361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
2.831 Γ— 10⁹⁡(96-digit number)
28312361659180958095…81964160509821918721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
5.662 Γ— 10⁹⁡(96-digit number)
56624723318361916191…63928321019643837441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.132 Γ— 10⁹⁢(97-digit number)
11324944663672383238…27856642039287674881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.264 Γ— 10⁹⁢(97-digit number)
22649889327344766476…55713284078575349761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
4.529 Γ— 10⁹⁢(97-digit number)
45299778654689532953…11426568157150699521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
9.059 Γ— 10⁹⁢(97-digit number)
90599557309379065906…22853136314301399041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.811 Γ— 10⁹⁷(98-digit number)
18119911461875813181…45706272628602798081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
3.623 Γ— 10⁹⁷(98-digit number)
36239822923751626362…91412545257205596161
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 2121524

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 d2253409ed20dd1b4db956d815f1d601ac800fd2f3ad8a0d2d03d1653ee4bcb0

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 #2,121,524 on Chainz β†—
Circulating Supply:57,890,579 XPMΒ·at block #6,830,805 Β· updates every 60s
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