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Block #755,372

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 10/7/2014, 11:04:02 AM Β· Difficulty 10.9679 Β· 6,057,115 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ded4d2f02ed9b98d07d8ba32634f483935387bca4ea94d02e33c41b2d139f7e
View on Chainz β†—

Height

#755,372

Difficulty

10.967947

Transactions

1

Size

243 B

Version

2

Bits

0af7cb66

Nonce

2,270,104,595

Timestamp

10/7/2014, 11:04:02 AM

Confirmations

6,057,115

Merkle Root

ce56da733fd22b6ed14b57c18f5545956f1231fce6423c1b3185a4c7473c2ede
Transactions (1)
Coinbasece56da733fd22b…85a4c7473c2ede
1 in β†’ 2 out8.3000 XPM152 B
AYFivgcJ…FT8wELGFALPu3s2c…EJXLjVFh
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.

2.609 Γ— 10⁹⁢(97-digit number)
26095608006957559094…90532766141095603520
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
2.609 Γ— 10⁹⁢(97-digit number)
26095608006957559094…90532766141095603521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.219 Γ— 10⁹⁢(97-digit number)
52191216013915118188…81065532282191207041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.043 Γ— 10⁹⁷(98-digit number)
10438243202783023637…62131064564382414081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.087 Γ— 10⁹⁷(98-digit number)
20876486405566047275…24262129128764828161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.175 Γ— 10⁹⁷(98-digit number)
41752972811132094550…48524258257529656321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
8.350 Γ— 10⁹⁷(98-digit number)
83505945622264189101…97048516515059312641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.670 Γ— 10⁹⁸(99-digit number)
16701189124452837820…94097033030118625281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.340 Γ— 10⁹⁸(99-digit number)
33402378248905675640…88194066060237250561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
6.680 Γ— 10⁹⁸(99-digit number)
66804756497811351280…76388132120474501121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.336 Γ— 10⁹⁹(100-digit number)
13360951299562270256…52776264240949002241
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 755372

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 2ded4d2f02ed9b98d07d8ba32634f483935387bca4ea94d02e33c41b2d139f7e

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 #755,372 on Chainz β†—
Circulating Supply:57,743,925 XPMΒ·at block #6,812,486 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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