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Block #649,455

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 7/26/2014, 11:45:14 PM Β· Difficulty 10.9520 Β· 6,149,140 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d52d9b94e6aaf5bc5eb402ebde744d9b1758ba0de8d5d0f59289c6516aeb6ad3
View on Chainz β†—

Height

#649,455

Difficulty

10.952022

Transactions

2

Size

582 B

Version

2

Bits

0af3b7bd

Nonce

95,400,759

Timestamp

7/26/2014, 11:45:14 PM

Confirmations

6,149,140

Merkle Root

6d7e35e955d26c42e6d691a8fffbfcd112377283a93dcc89eb39505bbb53bdf0
Transactions (2)
Coinbaseba3edac40f28b2…184fde3195a93d
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
ab7693f13f74ba…a7b69b1a92ab6d
2 in β†’ 2 out1.0656 XPM375 B
AcdyemUU…wyL11368APw5fdRm…569qLdko
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.

4.623 Γ— 10⁹⁷(98-digit number)
46230710778594160751…57754205173657176560
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
4.623 Γ— 10⁹⁷(98-digit number)
46230710778594160751…57754205173657176561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
9.246 Γ— 10⁹⁷(98-digit number)
92461421557188321502…15508410347314353121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.849 Γ— 10⁹⁸(99-digit number)
18492284311437664300…31016820694628706241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
3.698 Γ— 10⁹⁸(99-digit number)
36984568622875328600…62033641389257412481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
7.396 Γ— 10⁹⁸(99-digit number)
73969137245750657201…24067282778514824961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
1.479 Γ— 10⁹⁹(100-digit number)
14793827449150131440…48134565557029649921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
2.958 Γ— 10⁹⁹(100-digit number)
29587654898300262880…96269131114059299841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
5.917 Γ— 10⁹⁹(100-digit number)
59175309796600525761…92538262228118599681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
1.183 Γ— 10¹⁰⁰(101-digit number)
11835061959320105152…85076524456237199361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
2.367 Γ— 10¹⁰⁰(101-digit number)
23670123918640210304…70153048912474398721
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 649455

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 d52d9b94e6aaf5bc5eb402ebde744d9b1758ba0de8d5d0f59289c6516aeb6ad3

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 #649,455 on Chainz β†—
Circulating Supply:57,632,774 XPMΒ·at block #6,798,594 Β· updates every 60s
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