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Home/Chain Registry/Block #1,407,276

Block #1,407,276

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 1/10/2016, 12:04:24 PM Β· Difficulty 10.8057 Β· 5,435,911 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c8487261de181e4c1524503f3529cd3d3e23e8e8559a48b43e8fe6b3cc5e32d8
View on Chainz β†—

Difficulty

10.805749

Transactions

1

Size

199 B

Version

2

Bits

0ace458e

Nonce

414,970,204

Timestamp

1/10/2016, 12:04:24 PM

Confirmations

5,435,911

Merkle Root

ebf7bd7dfa3d6ba6b884ff0afc45e5314fb14fa3123368123eaccf69d7f8c6f7
Transactions (1)
Coinbaseebf7bd7dfa3d6b…accf69d7f8c6f7
1 in β†’ 1 out8.5500 XPM109 B
ANZEVh2v…Ao6G3jCA
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.

1.160 Γ— 10⁹⁴(95-digit number)
11608639356864739553…63592705153441340680
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
1.160 Γ— 10⁹⁴(95-digit number)
11608639356864739553…63592705153441340681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.321 Γ— 10⁹⁴(95-digit number)
23217278713729479106…27185410306882681361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
4.643 Γ— 10⁹⁴(95-digit number)
46434557427458958213…54370820613765362721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
9.286 Γ— 10⁹⁴(95-digit number)
92869114854917916427…08741641227530725441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.857 Γ— 10⁹⁡(96-digit number)
18573822970983583285…17483282455061450881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.714 Γ— 10⁹⁡(96-digit number)
37147645941967166570…34966564910122901761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
7.429 Γ— 10⁹⁡(96-digit number)
74295291883934333141…69933129820245803521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.485 Γ— 10⁹⁢(97-digit number)
14859058376786866628…39866259640491607041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.971 Γ— 10⁹⁢(97-digit number)
29718116753573733256…79732519280983214081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.943 Γ— 10⁹⁢(97-digit number)
59436233507147466513…59465038561966428161
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 1407276

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 c8487261de181e4c1524503f3529cd3d3e23e8e8559a48b43e8fe6b3cc5e32d8

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 #1,407,276 on Chainz β†—
Circulating Supply:57,989,864 XPMΒ·at block #6,843,186 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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