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Home/Chain Registry/Block #2,130,031

Block #2,130,031

1CCLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Cunningham Chain of the First Kind Ā· Discovered 5/24/2017, 3:53:03 AM Ā· Difficulty 10.9094 Ā· 4,708,101 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
99b951d827400dec96c7cc7b15a2c16c93daa5ff1ecd1fda4ca686b412b817df
View on Chainz ā†—

Difficulty

10.909407

Transactions

3

Size

651 B

Version

2

Bits

0ae8cee2

Nonce

1,910,432,986

Timestamp

5/24/2017, 3:53:03 AM

Confirmations

4,708,101

Merkle Root

98cc42c41db25ae4f37300bfcd73a742d6079778a2683a5a36785e443e919462
Transactions (3)
Coinbaseb69f9f99e45355ā€¦b5d5274cbc6b4f
1 in ā†’ 1 out8.4100 XPM110 B
AVGtE3Y1ā€¦SN8vShrN
5c85c6d32af854ā€¦3a67477e5c4a3c
1 in ā†’ 2 out289795.3889 XPM226 B
AP6fvXoQā€¦zwFkdkzJAWFpuxbDā€¦vM9iRbid
aa884580000cc4ā€¦c657d9056b6744
1 in ā†’ 2 out200133.3925 XPM226 B
AHsmZBjCā€¦sxzdcF2gAXgC7Kohā€¦fUARpSbK
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.633 Ɨ 10ā¹Ā³(94-digit number)
26331457979998731425ā€¦06180270493692043880
Discovered Prime Numbers
p_k = 2^k Ɨ origin āˆ’ 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 āˆ’ 1
2.633 Ɨ 10ā¹Ā³(94-digit number)
26331457979998731425ā€¦06180270493692043879
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2+1 ā†’
2
2^1 Ɨ origin āˆ’ 1
5.266 Ɨ 10ā¹Ā³(94-digit number)
52662915959997462850ā€¦12360540987384087759
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2+1 ā†’
3
2^2 Ɨ origin āˆ’ 1
1.053 Ɨ 10ā¹ā“(95-digit number)
10532583191999492570ā€¦24721081974768175519
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2+1 ā†’
4
2^3 Ɨ origin āˆ’ 1
2.106 Ɨ 10ā¹ā“(95-digit number)
21065166383998985140ā€¦49442163949536351039
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2+1 ā†’
5
2^4 Ɨ origin āˆ’ 1
4.213 Ɨ 10ā¹ā“(95-digit number)
42130332767997970280ā€¦98884327899072702079
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2+1 ā†’
6
2^5 Ɨ origin āˆ’ 1
8.426 Ɨ 10ā¹ā“(95-digit number)
84260665535995940560ā€¦97768655798145404159
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2+1 ā†’
7
2^6 Ɨ origin āˆ’ 1
1.685 Ɨ 10ā¹āµ(96-digit number)
16852133107199188112ā€¦95537311596290808319
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2+1 ā†’
8
2^7 Ɨ origin āˆ’ 1
3.370 Ɨ 10ā¹āµ(96-digit number)
33704266214398376224ā€¦91074623192581616639
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2+1 ā†’
9
2^8 Ɨ origin āˆ’ 1
6.740 Ɨ 10ā¹āµ(96-digit number)
67408532428796752448ā€¦82149246385163233279
Verify on FactorDB ā†—Wolfram Alpha ā†—
Ɨ2+1 ā†’
10
2^9 Ɨ origin āˆ’ 1
1.348 Ɨ 10ā¹ā¶(97-digit number)
13481706485759350489ā€¦64298492770326466559
Verify on FactorDB ā†—Wolfram Alpha ā†—

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 ā€” the large number shown above ā€” 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 ā†’
ā˜…ā˜…ā˜†ā˜†ā˜†
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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: pā‚ (first prime), pā‚‚ = 2pā‚ + 1, pā‚ƒ = 2pā‚‚ + 1, ā€¦
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 2130031

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 99b951d827400dec96c7cc7b15a2c16c93daa5ff1ecd1fda4ca686b412b817df

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 ā†’ Debug Window ā†’ 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 #2,130,031 on Chainz ā†—
Circulating Supply:57,949,323 XPMĀ·at block #6,838,131 Ā· updates every 60s
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