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Block #213,453

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/16/2013, 9:20:32 PM Β· Difficulty 9.9215 Β· 6,582,200 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
92a0c521a2bd71ff58c6c7d55f673665f9a98ccb86effc86e2dbbc3a104ae2c9
View on Chainz β†—

Height

#213,453

Difficulty

9.921539

Transactions

2

Size

719 B

Version

2

Bits

09ebe9f7

Nonce

37,997

Timestamp

10/16/2013, 9:20:32 PM

Confirmations

6,582,200

Merkle Root

390943e123b2fb0a692d0ceb92ac156bc85dcce4189286a30a8cd6f0cba43b53
Transactions (2)
Coinbase26f1a2da4353ff…84d387a993a37d
1 in β†’ 1 out10.1600 XPM109 B
AYxoZR2t…djGFFyWL
19165e6f17d931…47b92afc0f90b9
3 in β†’ 2 out2512.1193 XPM521 B
Ae4wBGtM…TBBWvZYvAM4M1K2v…H8xfBx5T
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.

1.546 Γ— 10⁹³(94-digit number)
15469582116197989872…76368711347676151190
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
1.546 Γ— 10⁹³(94-digit number)
15469582116197989872…76368711347676151191
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
3.093 Γ— 10⁹³(94-digit number)
30939164232395979744…52737422695352302381
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
6.187 Γ— 10⁹³(94-digit number)
61878328464791959489…05474845390704604761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.237 Γ— 10⁹⁴(95-digit number)
12375665692958391897…10949690781409209521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.475 Γ— 10⁹⁴(95-digit number)
24751331385916783795…21899381562818419041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.950 Γ— 10⁹⁴(95-digit number)
49502662771833567591…43798763125636838081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.900 Γ— 10⁹⁴(95-digit number)
99005325543667135182…87597526251273676161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.980 Γ— 10⁹⁡(96-digit number)
19801065108733427036…75195052502547352321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.960 Γ— 10⁹⁡(96-digit number)
39602130217466854073…50390105005094704641
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 213453

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 92a0c521a2bd71ff58c6c7d55f673665f9a98ccb86effc86e2dbbc3a104ae2c9

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 #213,453 on Chainz β†—
Circulating Supply:57,609,295 XPMΒ·at block #6,795,652 Β· updates every 60s
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