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Home/Chain Registry/Block #1,416,087

Block #1,416,087

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/16/2016, 6:29:02 PM Β· Difficulty 10.7976 Β· 5,422,391 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
793269f38c680f238a645a7ca71412fbed28d94180a21a9625a85c15153f8bf1
View on Chainz β†—

Difficulty

10.797636

Transactions

1

Size

200 B

Version

2

Bits

0acc31d9

Nonce

115,101,381

Timestamp

1/16/2016, 6:29:02 PM

Confirmations

5,422,391

Merkle Root

6360c5e9c3670df407c76e793101243aa9bf4f07c722800faef14f200efec1ff
Transactions (1)
Coinbase6360c5e9c3670d…f14f200efec1ff
1 in β†’ 1 out8.5600 XPM109 B
AdgfY2AF…8ZfgCxug
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.

6.714 Γ— 10⁹⁢(97-digit number)
67149095442780826930…36907521115976350720
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
6.714 Γ— 10⁹⁢(97-digit number)
67149095442780826930…36907521115976350719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.342 Γ— 10⁹⁷(98-digit number)
13429819088556165386…73815042231952701439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.685 Γ— 10⁹⁷(98-digit number)
26859638177112330772…47630084463905402879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
5.371 Γ— 10⁹⁷(98-digit number)
53719276354224661544…95260168927810805759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.074 Γ— 10⁹⁸(99-digit number)
10743855270844932308…90520337855621611519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.148 Γ— 10⁹⁸(99-digit number)
21487710541689864617…81040675711243223039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
4.297 Γ— 10⁹⁸(99-digit number)
42975421083379729235…62081351422486446079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
8.595 Γ— 10⁹⁸(99-digit number)
85950842166759458471…24162702844972892159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.719 Γ— 10⁹⁹(100-digit number)
17190168433351891694…48325405689945784319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
3.438 Γ— 10⁹⁹(100-digit number)
34380336866703783388…96650811379891568639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
6.876 Γ— 10⁹⁹(100-digit number)
68760673733407566777…93301622759783137279
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 1416087

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 793269f38c680f238a645a7ca71412fbed28d94180a21a9625a85c15153f8bf1

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 #1,416,087 on Chainz β†—
Circulating Supply:57,952,095 XPMΒ·at block #6,838,477 Β· updates every 60s
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