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Home/Chain Registry/Block #2,151,816

Block #2,151,816

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 6/8/2017, 3:35:50 PM Β· Difficulty 10.9003 Β· 4,660,362 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f328de0e11c2d6546fbf0b0fe06b2f574e81c495cdd94eb0bdebe2db963d9985
View on Chainz β†—

Difficulty

10.900252

Transactions

1

Size

200 B

Version

2

Bits

0ae676eb

Nonce

1,142,727,924

Timestamp

6/8/2017, 3:35:50 PM

Confirmations

4,660,362

Merkle Root

8400433a54c4c37973f076356709b7afeb8c2c60c03e7cb4f4b1f5803c82bbd5
Transactions (1)
Coinbase8400433a54c4c3…b1f5803c82bbd5
1 in β†’ 1 out8.4000 XPM110 B
AcR3KvMj…JpCP6BQi
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.

5.764 Γ— 10⁹⁴(95-digit number)
57645881394268627138…63031303854103603600
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
5.764 Γ— 10⁹⁴(95-digit number)
57645881394268627138…63031303854103603599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
1.152 Γ— 10⁹⁡(96-digit number)
11529176278853725427…26062607708207207199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
2.305 Γ— 10⁹⁡(96-digit number)
23058352557707450855…52125215416414414399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
4.611 Γ— 10⁹⁡(96-digit number)
46116705115414901710…04250430832828828799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
9.223 Γ— 10⁹⁡(96-digit number)
92233410230829803420…08500861665657657599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.844 Γ— 10⁹⁢(97-digit number)
18446682046165960684…17001723331315315199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
3.689 Γ— 10⁹⁢(97-digit number)
36893364092331921368…34003446662630630399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
7.378 Γ— 10⁹⁢(97-digit number)
73786728184663842736…68006893325261260799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.475 Γ— 10⁹⁷(98-digit number)
14757345636932768547…36013786650522521599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.951 Γ— 10⁹⁷(98-digit number)
29514691273865537094…72027573301045043199
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 2151816

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 f328de0e11c2d6546fbf0b0fe06b2f574e81c495cdd94eb0bdebe2db963d9985

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 #2,151,816 on Chainz β†—
Circulating Supply:57,741,444 XPMΒ·at block #6,812,177 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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