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Home/Chain Registry/Block #2,156,012

Block #2,156,012

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/11/2017, 9:01:07 AM Β· Difficulty 10.9056 Β· 4,684,286 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1109f40679a0cf70b6758190f1068d0e0d02d2f07c7a5f507eb95ba517678deb
View on Chainz β†—

Difficulty

10.905601

Transactions

1

Size

208 B

Version

2

Bits

0ae7d578

Nonce

113,797,242

Timestamp

6/11/2017, 9:01:07 AM

Confirmations

4,684,286

Merkle Root

bca6c14dacf9138d3594f5710674e45d35b56a06659c6ffde9f3f7b2ae3e0d2d
Transactions (1)
Coinbasebca6c14dacf913…f3f7b2ae3e0d2d
1 in β†’ 1 out8.3900 XPM118 B
AM6GYpjw…aw86QDtR
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.

9.207 Γ— 10⁹⁴(95-digit number)
92079675371573663238…74935968164882673280
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
9.207 Γ— 10⁹⁴(95-digit number)
92079675371573663238…74935968164882673279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.841 Γ— 10⁹⁡(96-digit number)
18415935074314732647…49871936329765346559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.683 Γ— 10⁹⁡(96-digit number)
36831870148629465295…99743872659530693119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
7.366 Γ— 10⁹⁡(96-digit number)
73663740297258930590…99487745319061386239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.473 Γ— 10⁹⁢(97-digit number)
14732748059451786118…98975490638122772479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.946 Γ— 10⁹⁢(97-digit number)
29465496118903572236…97950981276245544959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.893 Γ— 10⁹⁢(97-digit number)
58930992237807144472…95901962552491089919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.178 Γ— 10⁹⁷(98-digit number)
11786198447561428894…91803925104982179839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.357 Γ— 10⁹⁷(98-digit number)
23572396895122857789…83607850209964359679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.714 Γ— 10⁹⁷(98-digit number)
47144793790245715578…67215700419928719359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
9.428 Γ— 10⁹⁷(98-digit number)
94289587580491431156…34431400839857438719
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 2156012

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 1109f40679a0cf70b6758190f1068d0e0d02d2f07c7a5f507eb95ba517678deb

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 #2,156,012 on Chainz β†—
Circulating Supply:57,966,700 XPMΒ·at block #6,840,297 Β· updates every 60s
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