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Home/Chain Registry/Block #2,703,373

Block #2,703,373

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/13/2018, 7:31:04 AM Β· Difficulty 11.6290 Β· 4,137,929 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ef6b0f200aa7752fc8512f635bb43ce96b88499011078441a83d6dac1859fff7
View on Chainz β†—

Difficulty

11.629004

Transactions

1

Size

200 B

Version

2

Bits

0ba10660

Nonce

786,018,895

Timestamp

6/13/2018, 7:31:04 AM

Confirmations

4,137,929

Merkle Root

101579609cadbcdb9895a2fd472dd6305f3c1e0e3420a34bc0c46444ae7bddb6
Transactions (1)
Coinbase101579609cadbc…c46444ae7bddb6
1 in β†’ 1 out7.3800 XPM110 B
AZtxQr2F…7grUWrUz
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.

6.486 Γ— 10⁹⁴(95-digit number)
64863508651680141299…80320865813065438840
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
6.486 Γ— 10⁹⁴(95-digit number)
64863508651680141299…80320865813065438839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.297 Γ— 10⁹⁡(96-digit number)
12972701730336028259…60641731626130877679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.594 Γ— 10⁹⁡(96-digit number)
25945403460672056519…21283463252261755359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.189 Γ— 10⁹⁡(96-digit number)
51890806921344113039…42566926504523510719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.037 Γ— 10⁹⁢(97-digit number)
10378161384268822607…85133853009047021439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.075 Γ— 10⁹⁢(97-digit number)
20756322768537645215…70267706018094042879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.151 Γ— 10⁹⁢(97-digit number)
41512645537075290431…40535412036188085759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.302 Γ— 10⁹⁢(97-digit number)
83025291074150580863…81070824072376171519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.660 Γ— 10⁹⁷(98-digit number)
16605058214830116172…62141648144752343039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.321 Γ— 10⁹⁷(98-digit number)
33210116429660232345…24283296289504686079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.642 Γ— 10⁹⁷(98-digit number)
66420232859320464690…48566592579009372159
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 2703373

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 ef6b0f200aa7752fc8512f635bb43ce96b88499011078441a83d6dac1859fff7

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 #2,703,373 on Chainz β†—
Circulating Supply:57,974,775 XPMΒ·at block #6,841,301 Β· updates every 60s
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