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Home/Chain Registry/Block #2,169,057

Block #2,169,057

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/20/2017, 4:41:41 PM Β· Difficulty 10.8987 Β· 4,663,992 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d493b38af8fb946a97df19744d42699803522d112ca7d273d6890ba272090b15
View on Chainz β†—

Difficulty

10.898737

Transactions

3

Size

3.89 KB

Version

2

Bits

0ae613a6

Nonce

927,825,154

Timestamp

6/20/2017, 4:41:41 PM

Confirmations

4,663,992

Merkle Root

66b3058929956f8ceea9f21487f9bfa9e044193673ec583df66d7c21007367ba
Transactions (3)
Coinbaseea06fb6fbeb402…6e3b49da599c87
1 in β†’ 1 out8.4600 XPM110 B
AJvRA39R…WaCoejFm
49a957abb58e72…6df76ffaaf91d3
3 in β†’ 1 out10599.9900 XPM488 B
ANr6pCrE…r8E74V74
b765e73b121a0a…a60ac4df5bd30f
22 in β†’ 1 out155.9600 XPM3.22 KB
AZE4Pwgy…KNsYdSoQ
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.

4.446 Γ— 10⁹⁴(95-digit number)
44463794051927430128…38001304578495911240
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
4.446 Γ— 10⁹⁴(95-digit number)
44463794051927430128…38001304578495911239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
8.892 Γ— 10⁹⁴(95-digit number)
88927588103854860257…76002609156991822479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.778 Γ— 10⁹⁡(96-digit number)
17785517620770972051…52005218313983644959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.557 Γ— 10⁹⁡(96-digit number)
35571035241541944103…04010436627967289919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.114 Γ— 10⁹⁡(96-digit number)
71142070483083888206…08020873255934579839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.422 Γ— 10⁹⁢(97-digit number)
14228414096616777641…16041746511869159679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.845 Γ— 10⁹⁢(97-digit number)
28456828193233555282…32083493023738319359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.691 Γ— 10⁹⁢(97-digit number)
56913656386467110565…64166986047476638719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.138 Γ— 10⁹⁷(98-digit number)
11382731277293422113…28333972094953277439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.276 Γ— 10⁹⁷(98-digit number)
22765462554586844226…56667944189906554879
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 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
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 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 2169057

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 d493b38af8fb946a97df19744d42699803522d112ca7d273d6890ba272090b15

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 #2,169,057 on Chainz β†—
Circulating Supply:57,908,572 XPMΒ·at block #6,833,048 Β· updates every 60s
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