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Block #268,607

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/22/2013, 6:39:12 AM Β· Difficulty 9.9569 Β· 6,543,848 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
eb6307e75e7651b1f87663e792da5a53c9931ad81354a4a9dc35f6b782c0deec
View on Chainz β†—

Height

#268,607

Difficulty

9.956935

Transactions

1

Size

187 B

Version

2

Bits

09f4f9a9

Nonce

96,156

Timestamp

11/22/2013, 6:39:12 AM

Confirmations

6,543,848

Merkle Root

5076116f6cc7dc8ec2b2bc63ab365fd3052428d5b16f31b04d7931ed059a79ca
Transactions (1)
Coinbase5076116f6cc7dc…7931ed059a79ca
1 in β†’ 1 out10.0700 XPM97 B
AXz615Ej…Sy5yeWWM
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.

2.735 Γ— 10⁹⁴(95-digit number)
27351074076759037364…49065350534775879680
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
2.735 Γ— 10⁹⁴(95-digit number)
27351074076759037364…49065350534775879681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.470 Γ— 10⁹⁴(95-digit number)
54702148153518074728…98130701069551759361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.094 Γ— 10⁹⁡(96-digit number)
10940429630703614945…96261402139103518721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.188 Γ— 10⁹⁡(96-digit number)
21880859261407229891…92522804278207037441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.376 Γ— 10⁹⁡(96-digit number)
43761718522814459782…85045608556414074881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.752 Γ— 10⁹⁡(96-digit number)
87523437045628919565…70091217112828149761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.750 Γ— 10⁹⁢(97-digit number)
17504687409125783913…40182434225656299521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.500 Γ— 10⁹⁢(97-digit number)
35009374818251567826…80364868451312599041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.001 Γ— 10⁹⁢(97-digit number)
70018749636503135652…60729736902625198081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.400 Γ— 10⁹⁷(98-digit number)
14003749927300627130…21459473805250396161
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 268607

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 eb6307e75e7651b1f87663e792da5a53c9931ad81354a4a9dc35f6b782c0deec

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 #268,607 on Chainz β†—
Circulating Supply:57,743,664 XPMΒ·at block #6,812,454 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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