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Home/Chain Registry/Block #2,716,656

Block #2,716,656

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/22/2018, 4:27:58 PM Β· Difficulty 11.6134 Β· 4,115,168 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b6126cd2e3167c2cb2c61bcdd025792ce9fb1d8cb9d25e8d57f6f2e88cffa7c0
View on Chainz β†—

Difficulty

11.613436

Transactions

2

Size

1.03 KB

Version

2

Bits

0b9d0a2c

Nonce

712,302,640

Timestamp

6/22/2018, 4:27:58 PM

Confirmations

4,115,168

Merkle Root

2382c169dc618b260b64d6385279ebd485dc8c0ff8c1420f0e0d8dfa42131da4
Transactions (2)
Coinbase73a14e1cf1981d…f203c3bdc98293
1 in β†’ 1 out7.4100 XPM110 B
AZtxQr2F…7grUWrUz
c7f409564892fc…7baacb39358efe
5 in β†’ 3 out2483.7336 XPM853 B
AbKFvGKV…eL3bdfEbARywRRZa…HVd3P31RAbjWY44z…dfKv2aig
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.

4.860 Γ— 10⁹⁴(95-digit number)
48607918799675592068…35271799888721681280
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
4.860 Γ— 10⁹⁴(95-digit number)
48607918799675592068…35271799888721681279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.721 Γ— 10⁹⁴(95-digit number)
97215837599351184137…70543599777443362559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.944 Γ— 10⁹⁡(96-digit number)
19443167519870236827…41087199554886725119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.888 Γ— 10⁹⁡(96-digit number)
38886335039740473654…82174399109773450239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.777 Γ— 10⁹⁡(96-digit number)
77772670079480947309…64348798219546900479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.555 Γ— 10⁹⁢(97-digit number)
15554534015896189461…28697596439093800959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.110 Γ— 10⁹⁢(97-digit number)
31109068031792378923…57395192878187601919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.221 Γ— 10⁹⁢(97-digit number)
62218136063584757847…14790385756375203839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.244 Γ— 10⁹⁷(98-digit number)
12443627212716951569…29580771512750407679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.488 Γ— 10⁹⁷(98-digit number)
24887254425433903139…59161543025500815359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
4.977 Γ— 10⁹⁷(98-digit number)
49774508850867806278…18323086051001630719
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 2716656

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 b6126cd2e3167c2cb2c61bcdd025792ce9fb1d8cb9d25e8d57f6f2e88cffa7c0

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 #2,716,656 on Chainz β†—
Circulating Supply:57,898,709 XPMΒ·at block #6,831,823 Β· updates every 60s
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