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Block #272,221

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/25/2013, 3:21:52 AM Β· Difficulty 9.9525 Β· 6,522,663 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1967c068b7cb57d7ffe39bb7146e6027e97c63fd3cd644ec4f0cddda14c0934b
View on Chainz β†—

Height

#272,221

Difficulty

9.952511

Transactions

2

Size

719 B

Version

2

Bits

09f3d7c9

Nonce

764

Timestamp

11/25/2013, 3:21:52 AM

Confirmations

6,522,663

Merkle Root

6b522db70e859355f9178aec294ce321ec5935eb4e7b31e4ee424c3301408fee
Transactions (2)
Coinbase7d90ac204193f4…d8d185d6f9a1c3
1 in β†’ 1 out10.0900 XPM109 B
AHPZwdfN…HY7Wvq9V
f39d01fe6e928d…546ddffbc0673c
3 in β†’ 2 out299.0100 XPM520 B
ATPM2yfs…AQmg5midAYt61rm7…WZjuMcPC
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.

9.257 Γ— 10⁹⁴(95-digit number)
92578075002543642206…30080708939613006080
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
9.257 Γ— 10⁹⁴(95-digit number)
92578075002543642206…30080708939613006081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.851 Γ— 10⁹⁡(96-digit number)
18515615000508728441…60161417879226012161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.703 Γ— 10⁹⁡(96-digit number)
37031230001017456882…20322835758452024321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.406 Γ— 10⁹⁡(96-digit number)
74062460002034913765…40645671516904048641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.481 Γ— 10⁹⁢(97-digit number)
14812492000406982753…81291343033808097281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.962 Γ— 10⁹⁢(97-digit number)
29624984000813965506…62582686067616194561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.924 Γ— 10⁹⁢(97-digit number)
59249968001627931012…25165372135232389121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.184 Γ— 10⁹⁷(98-digit number)
11849993600325586202…50330744270464778241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.369 Γ— 10⁹⁷(98-digit number)
23699987200651172404…00661488540929556481
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 272221

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 1967c068b7cb57d7ffe39bb7146e6027e97c63fd3cd644ec4f0cddda14c0934b

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 #272,221 on Chainz β†—
Circulating Supply:57,603,107 XPMΒ·at block #6,794,883 Β· updates every 60s
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