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Block #857,139

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/17/2014, 2:57:36 PM Β· Difficulty 10.9677 Β· 5,988,246 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
faeee1b12d0b3c56d66f32ba17f3c9e0d4dd754d545f238d53e7a1f016a15393
View on Chainz β†—

Height

#857,139

Difficulty

10.967652

Transactions

1

Size

242 B

Version

2

Bits

0af7b80c

Nonce

482,608,734

Timestamp

12/17/2014, 2:57:36 PM

Confirmations

5,988,246

Merkle Root

01c482ca661064b300972c1abf554716e1383399b7b55e6e5ec8c5ffccce0888
Transactions (1)
Coinbase01c482ca661064…c8c5ffccce0888
1 in β†’ 2 out8.3000 XPM152 B
AYaoTAKj…bg6UXCe3ALPu3s2c…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.

5.309 Γ— 10⁹⁡(96-digit number)
53094694103564041510…76737074920234220640
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
5.309 Γ— 10⁹⁡(96-digit number)
53094694103564041510…76737074920234220639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.061 Γ— 10⁹⁢(97-digit number)
10618938820712808302…53474149840468441279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.123 Γ— 10⁹⁢(97-digit number)
21237877641425616604…06948299680936882559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.247 Γ— 10⁹⁢(97-digit number)
42475755282851233208…13896599361873765119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
8.495 Γ— 10⁹⁢(97-digit number)
84951510565702466417…27793198723747530239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.699 Γ— 10⁹⁷(98-digit number)
16990302113140493283…55586397447495060479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.398 Γ— 10⁹⁷(98-digit number)
33980604226280986567…11172794894990120959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
6.796 Γ— 10⁹⁷(98-digit number)
67961208452561973134…22345589789980241919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.359 Γ— 10⁹⁸(99-digit number)
13592241690512394626…44691179579960483839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.718 Γ— 10⁹⁸(99-digit number)
27184483381024789253…89382359159920967679
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 857139

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 faeee1b12d0b3c56d66f32ba17f3c9e0d4dd754d545f238d53e7a1f016a15393

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 #857,139 on Chainz β†—
Circulating Supply:58,007,524 XPMΒ·at block #6,845,384 Β· updates every 60s
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