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Block #847,007

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/10/2014, 1:07:50 AM Β· Difficulty 10.9720 Β· 5,997,593 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
bd8ac8045a845ddceca53054334f86fe4e98e5e8509254ff29f215e2ac548a58
View on Chainz β†—

Height

#847,007

Difficulty

10.971991

Transactions

1

Size

243 B

Version

2

Bits

0af8d460

Nonce

1,108,754,908

Timestamp

12/10/2014, 1:07:50 AM

Confirmations

5,997,593

Merkle Root

4a14e17d13783d6f9d94c0e2fa874b45d94ff3bff6e232e06d926c33bdf5518c
Transactions (1)
Coinbase4a14e17d13783d…926c33bdf5518c
1 in β†’ 2 out8.2900 XPM152 B
ATKA59X6…uuBWgZSXALPu3s2c…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.

2.193 Γ— 10⁹⁢(97-digit number)
21935591115155439784…77212410353638309600
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
2.193 Γ— 10⁹⁢(97-digit number)
21935591115155439784…77212410353638309599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.387 Γ— 10⁹⁢(97-digit number)
43871182230310879569…54424820707276619199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.774 Γ— 10⁹⁢(97-digit number)
87742364460621759138…08849641414553238399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.754 Γ— 10⁹⁷(98-digit number)
17548472892124351827…17699282829106476799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.509 Γ— 10⁹⁷(98-digit number)
35096945784248703655…35398565658212953599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.019 Γ— 10⁹⁷(98-digit number)
70193891568497407310…70797131316425907199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.403 Γ— 10⁹⁸(99-digit number)
14038778313699481462…41594262632851814399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.807 Γ— 10⁹⁸(99-digit number)
28077556627398962924…83188525265703628799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.615 Γ— 10⁹⁸(99-digit number)
56155113254797925848…66377050531407257599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.123 Γ— 10⁹⁹(100-digit number)
11231022650959585169…32754101062814515199
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 847007

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 bd8ac8045a845ddceca53054334f86fe4e98e5e8509254ff29f215e2ac548a58

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 #847,007 on Chainz β†—
Circulating Supply:58,001,210 XPMΒ·at block #6,844,599 Β· updates every 60s
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