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Block #1,356,456

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/5/2015, 9:39:17 PM Β· Difficulty 10.8203 Β· 5,444,664 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c7fa1ea1c9cc7687ae600d83fdb07cfa41fd16f1a13c9d519c0e4c58c37858cf
View on Chainz β†—

Difficulty

10.820329

Transactions

1

Size

243 B

Version

2

Bits

0ad2010f

Nonce

305,090,149

Timestamp

12/5/2015, 9:39:17 PM

Confirmations

5,444,664

Merkle Root

3aa7b493335c90d7dcd16cfd6f556be1fa816316cf664385dafcb1c45b320fd9
Transactions (1)
Coinbase3aa7b493335c90…fcb1c45b320fd9
1 in β†’ 2 out8.5300 XPM152 B
AaC6Y3Hw…9BJgUQ4DALPu3s2c…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.

1.246 Γ— 10⁹⁷(98-digit number)
12460472725094677250…93608190953220899840
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
1.246 Γ— 10⁹⁷(98-digit number)
12460472725094677250…93608190953220899839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.492 Γ— 10⁹⁷(98-digit number)
24920945450189354501…87216381906441799679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.984 Γ— 10⁹⁷(98-digit number)
49841890900378709003…74432763812883599359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
9.968 Γ— 10⁹⁷(98-digit number)
99683781800757418007…48865527625767198719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.993 Γ— 10⁹⁸(99-digit number)
19936756360151483601…97731055251534397439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.987 Γ— 10⁹⁸(99-digit number)
39873512720302967203…95462110503068794879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.974 Γ— 10⁹⁸(99-digit number)
79747025440605934406…90924221006137589759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.594 Γ— 10⁹⁹(100-digit number)
15949405088121186881…81848442012275179519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.189 Γ— 10⁹⁹(100-digit number)
31898810176242373762…63696884024550359039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.379 Γ— 10⁹⁹(100-digit number)
63797620352484747524…27393768049100718079
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1356456

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 c7fa1ea1c9cc7687ae600d83fdb07cfa41fd16f1a13c9d519c0e4c58c37858cf

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 #1,356,456 on Chainz β†—
Circulating Supply:57,653,028 XPMΒ·at block #6,801,119 Β· updates every 60s
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