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Block #907,017

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/23/2015, 7:38:28 PM Β· Difficulty 10.9353 Β· 5,907,918 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3f5d56c8a0293808a67e54b236cb55848d80f3c7477e9f37154f01dfa2913b0f
View on Chainz β†—

Height

#907,017

Difficulty

10.935262

Transactions

1

Size

206 B

Version

2

Bits

0aef6d56

Nonce

44,082,106

Timestamp

1/23/2015, 7:38:28 PM

Confirmations

5,907,918

Merkle Root

e4f58e07465026157a825b014103018ef5b5ec2887c3183d8cf765ba1eb63fe8
Transactions (1)
Coinbasee4f58e07465026…f765ba1eb63fe8
1 in β†’ 1 out8.3500 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.265 Γ— 10⁹⁡(96-digit number)
22651408255346406434…44252653434385616500
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
2.265 Γ— 10⁹⁡(96-digit number)
22651408255346406434…44252653434385616499
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.530 Γ— 10⁹⁡(96-digit number)
45302816510692812868…88505306868771232999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
9.060 Γ— 10⁹⁡(96-digit number)
90605633021385625736…77010613737542465999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.812 Γ— 10⁹⁢(97-digit number)
18121126604277125147…54021227475084931999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.624 Γ— 10⁹⁢(97-digit number)
36242253208554250294…08042454950169863999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
7.248 Γ— 10⁹⁢(97-digit number)
72484506417108500589…16084909900339727999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.449 Γ— 10⁹⁷(98-digit number)
14496901283421700117…32169819800679455999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.899 Γ— 10⁹⁷(98-digit number)
28993802566843400235…64339639601358911999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.798 Γ— 10⁹⁷(98-digit number)
57987605133686800471…28679279202717823999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.159 Γ— 10⁹⁸(99-digit number)
11597521026737360094…57358558405435647999
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 907017

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 3f5d56c8a0293808a67e54b236cb55848d80f3c7477e9f37154f01dfa2913b0f

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 #907,017 on Chainz β†—
Circulating Supply:57,763,575 XPMΒ·at block #6,814,934 Β· updates every 60s
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