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Block #251,070

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/8/2013, 7:56:41 PM Β· Difficulty 9.9694 Β· 6,565,163 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2f277debc7e0aad177277d7f7af468e8ed750c4e52488b3ba92eb1e738e10d00
View on Chainz β†—

Height

#251,070

Difficulty

9.969408

Transactions

1

Size

209 B

Version

2

Bits

09f82b18

Nonce

16,782,376

Timestamp

11/8/2013, 7:56:41 PM

Confirmations

6,565,163

Merkle Root

7ca3636e7a5946c2b461d219b28470a2feb6ca46eb54c9206ae96da43d754006
Transactions (1)
Coinbase7ca3636e7a5946…e96da43d754006
1 in β†’ 1 out10.0500 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.590 Γ— 10¹⁰²(103-digit number)
25908126028162511571…50639112653008800000
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
2.590 Γ— 10¹⁰²(103-digit number)
25908126028162511571…50639112653008800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.181 Γ— 10¹⁰²(103-digit number)
51816252056325023143…01278225306017600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.036 Γ— 10¹⁰³(104-digit number)
10363250411265004628…02556450612035200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.072 Γ— 10¹⁰³(104-digit number)
20726500822530009257…05112901224070400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.145 Γ— 10¹⁰³(104-digit number)
41453001645060018514…10225802448140800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.290 Γ— 10¹⁰³(104-digit number)
82906003290120037028…20451604896281600001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.658 Γ— 10¹⁰⁴(105-digit number)
16581200658024007405…40903209792563200001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.316 Γ— 10¹⁰⁴(105-digit number)
33162401316048014811…81806419585126400001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.632 Γ— 10¹⁰⁴(105-digit number)
66324802632096029623…63612839170252800001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.326 Γ— 10¹⁰⁡(106-digit number)
13264960526419205924…27225678340505600001
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 251070

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 2f277debc7e0aad177277d7f7af468e8ed750c4e52488b3ba92eb1e738e10d00

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 #251,070 on Chainz β†—
Circulating Supply:57,773,989 XPMΒ·at block #6,816,232 Β· updates every 60s
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