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Home/Chain Registry/Block #844,953

Block #844,953

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/8/2014, 12:43:11 PM Β· Difficulty 10.9727 Β· 5,995,597 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
dd3bd4721bad001d20dee1e175edc601ce010ea1c8531c0cf9a12d0f89e47fd7
View on Chainz β†—

Height

#844,953

Difficulty

10.972651

Transactions

2

Size

432 B

Version

2

Bits

0af8ffa6

Nonce

74,809,428

Timestamp

12/8/2014, 12:43:11 PM

Confirmations

5,995,597

Merkle Root

698719e50a65ee66a7dd4ec25f05dfd4e4363ae08d9be94ee92acf1e80c1f681
Transactions (2)
Coinbase1aac34c2ee6849…1b17515c6b1755
1 in β†’ 1 out8.3050 XPM116 B
ANSXnLY2…Sd25TjkD
45e933f88d91d3…e837064d2fa492
1 in β†’ 2 out0.0722 XPM226 B
AZ7LBnvh…sC6rwpaDAJZ36uD2…XLGdEZZz
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.

3.061 Γ— 10⁹³(94-digit number)
30615614792966970466…61038918419545485400
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
3.061 Γ— 10⁹³(94-digit number)
30615614792966970466…61038918419545485399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
6.123 Γ— 10⁹³(94-digit number)
61231229585933940932…22077836839090970799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.224 Γ— 10⁹⁴(95-digit number)
12246245917186788186…44155673678181941599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.449 Γ— 10⁹⁴(95-digit number)
24492491834373576373…88311347356363883199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.898 Γ— 10⁹⁴(95-digit number)
48984983668747152746…76622694712727766399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
9.796 Γ— 10⁹⁴(95-digit number)
97969967337494305492…53245389425455532799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.959 Γ— 10⁹⁡(96-digit number)
19593993467498861098…06490778850911065599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.918 Γ— 10⁹⁡(96-digit number)
39187986934997722196…12981557701822131199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
7.837 Γ— 10⁹⁡(96-digit number)
78375973869995444393…25963115403644262399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.567 Γ— 10⁹⁢(97-digit number)
15675194773999088878…51926230807288524799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
3.135 Γ— 10⁹⁢(97-digit number)
31350389547998177757…03852461614577049599
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the First 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
RareChain length 11
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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 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 844953

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 dd3bd4721bad001d20dee1e175edc601ce010ea1c8531c0cf9a12d0f89e47fd7

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 #844,953 on Chainz β†—
Circulating Supply:57,968,734 XPMΒ·at block #6,840,549 Β· updates every 60s
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