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Home/Chain Registry/Block #2,053,712

Block #2,053,712

1CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 4/4/2017, 5:26:16 AM Β· Difficulty 10.7779 Β· 4,789,101 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f3ac43e886eef7e28f639f495828fbd34b9a93f6538779b197465a19da043ca2
View on Chainz β†—

Difficulty

10.777933

Transactions

2

Size

837 B

Version

2

Bits

0ac72697

Nonce

877,785,451

Timestamp

4/4/2017, 5:26:16 AM

Confirmations

4,789,101

Merkle Root

cd12d345cddac2edb9d253644c843435eb2c09e198c131c0f4d11d8d8c11182d
Transactions (2)
Coinbase3fe8e66b67584d…5c85c3279cf701
1 in β†’ 1 out8.6000 XPM109 B
AGtTD2qX…ScGATAgd
587955b64d5a97…316affa212f8a3
4 in β†’ 1 out5399.9900 XPM638 B
AcBaooYt…xSomgUCF
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.

1.074 Γ— 10⁹⁡(96-digit number)
10748700572139555467…10919462361367936160
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
1.074 Γ— 10⁹⁡(96-digit number)
10748700572139555467…10919462361367936159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.149 Γ— 10⁹⁡(96-digit number)
21497401144279110935…21838924722735872319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.299 Γ— 10⁹⁡(96-digit number)
42994802288558221871…43677849445471744639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.598 Γ— 10⁹⁡(96-digit number)
85989604577116443742…87355698890943489279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.719 Γ— 10⁹⁢(97-digit number)
17197920915423288748…74711397781886978559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.439 Γ— 10⁹⁢(97-digit number)
34395841830846577496…49422795563773957119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.879 Γ— 10⁹⁢(97-digit number)
68791683661693154993…98845591127547914239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.375 Γ— 10⁹⁷(98-digit number)
13758336732338630998…97691182255095828479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.751 Γ— 10⁹⁷(98-digit number)
27516673464677261997…95382364510191656959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.503 Γ— 10⁹⁷(98-digit number)
55033346929354523994…90764729020383313919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
11
2^10 Γ— origin βˆ’ 1
1.100 Γ— 10⁹⁸(99-digit number)
11006669385870904798…81529458040766627839
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 2053712

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 f3ac43e886eef7e28f639f495828fbd34b9a93f6538779b197465a19da043ca2

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 #2,053,712 on Chainz β†—
Circulating Supply:57,986,844 XPMΒ·at block #6,842,812 Β· updates every 60s
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