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Home/Chain Registry/Block #2,138,798

Block #2,138,798

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/31/2017, 5:09:56 AM Β· Difficulty 10.8810 Β· 4,703,360 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e7b9c143b8c6630d373f01a7ef33f4c8293e540881ad951a3c680b63dcbbf8dc
View on Chainz β†—

Difficulty

10.881003

Transactions

1

Size

243 B

Version

2

Bits

0ae18972

Nonce

75,400,518

Timestamp

5/31/2017, 5:09:56 AM

Confirmations

4,703,360

Merkle Root

dbb98060f512b7dfee4c372246e153aa398938f82f61400d89118ff199b6efe4
Transactions (1)
Coinbasedbb98060f512b7…118ff199b6efe4
1 in β†’ 2 out8.4300 XPM152 B
AX552jX9…gDRZgjsXALPu3s2c…EJXLjVFh
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.

1.166 Γ— 10⁹⁷(98-digit number)
11665256729914768596…24170468843670097920
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
1.166 Γ— 10⁹⁷(98-digit number)
11665256729914768596…24170468843670097919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.333 Γ— 10⁹⁷(98-digit number)
23330513459829537192…48340937687340195839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.666 Γ— 10⁹⁷(98-digit number)
46661026919659074384…96681875374680391679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.332 Γ— 10⁹⁷(98-digit number)
93322053839318148768…93363750749360783359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.866 Γ— 10⁹⁸(99-digit number)
18664410767863629753…86727501498721566719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.732 Γ— 10⁹⁸(99-digit number)
37328821535727259507…73455002997443133439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.465 Γ— 10⁹⁸(99-digit number)
74657643071454519014…46910005994886266879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.493 Γ— 10⁹⁹(100-digit number)
14931528614290903802…93820011989772533759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.986 Γ— 10⁹⁹(100-digit number)
29863057228581807605…87640023979545067519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.972 Γ— 10⁹⁹(100-digit number)
59726114457163615211…75280047959090135039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.194 Γ— 10¹⁰⁰(101-digit number)
11945222891432723042…50560095918180270079
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 2138798

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 e7b9c143b8c6630d373f01a7ef33f4c8293e540881ad951a3c680b63dcbbf8dc

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 #2,138,798 on Chainz β†—
Circulating Supply:57,981,655 XPMΒ·at block #6,842,157 Β· updates every 60s
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