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Block #551,971

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 5/19/2014, 4:08:39 AM Β· Difficulty 10.9626 Β· 6,262,396 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
96f64252934aa7cfd0395c76705aa1db7448630598f5dce6ca24fa2b4f0ab2c6
View on Chainz β†—

Height

#551,971

Difficulty

10.962586

Transactions

2

Size

433 B

Version

2

Bits

0af66c09

Nonce

472,644,349

Timestamp

5/19/2014, 4:08:39 AM

Confirmations

6,262,396

Merkle Root

b5012e650a2ea9765754da25d429d263784c86c847f20727986624906ccc3c19
Transactions (2)
Coinbase3a300d6c9f2d15…4771aa9512a22b
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
16b0cd2268380a…4aedea8b680939
1 in β†’ 2 out10.9900 XPM226 B
APRVA92P…9MyJED7GAYKb4UBF…9iC3UEKB
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.

8.614 Γ— 10⁹⁷(98-digit number)
86148850880638497823…91613784385345607880
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
8.614 Γ— 10⁹⁷(98-digit number)
86148850880638497823…91613784385345607879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.722 Γ— 10⁹⁸(99-digit number)
17229770176127699564…83227568770691215759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
3.445 Γ— 10⁹⁸(99-digit number)
34459540352255399129…66455137541382431519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
6.891 Γ— 10⁹⁸(99-digit number)
68919080704510798258…32910275082764863039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.378 Γ— 10⁹⁹(100-digit number)
13783816140902159651…65820550165529726079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
2.756 Γ— 10⁹⁹(100-digit number)
27567632281804319303…31641100331059452159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
5.513 Γ— 10⁹⁹(100-digit number)
55135264563608638606…63282200662118904319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.102 Γ— 10¹⁰⁰(101-digit number)
11027052912721727721…26564401324237808639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.205 Γ— 10¹⁰⁰(101-digit number)
22054105825443455442…53128802648475617279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
4.410 Γ— 10¹⁰⁰(101-digit number)
44108211650886910885…06257605296951234559
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 551971

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 96f64252934aa7cfd0395c76705aa1db7448630598f5dce6ca24fa2b4f0ab2c6

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 #551,971 on Chainz β†—
Circulating Supply:57,758,993 XPMΒ·at block #6,814,366 Β· updates every 60s
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