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Home/Chain Registry/Block #1,476,157

Block #1,476,157

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 2/28/2016, 10:08:00 PM Β· Difficulty 10.6978 Β· 5,365,736 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
84a11246a50d89285943f2912f0d201c4a8050d85d27a6257f71e6a481ea8a1a
View on Chainz β†—

Difficulty

10.697750

Transactions

1

Size

201 B

Version

2

Bits

0ab29fc5

Nonce

561,084,474

Timestamp

2/28/2016, 10:08:00 PM

Confirmations

5,365,736

Merkle Root

aa8cd115bd0d613240bae9ac19ad0b31984ddfdd4e5af7a8d8b051a8cac829a7
Transactions (1)
Coinbaseaa8cd115bd0d61…b051a8cac829a7
1 in β†’ 1 out8.7200 XPM110 B
Abi3cvt1…k9EwpauC
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.

1.258 Γ— 10⁹⁢(97-digit number)
12580607820605022907…85161629896176834560
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
1.258 Γ— 10⁹⁢(97-digit number)
12580607820605022907…85161629896176834559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.516 Γ— 10⁹⁢(97-digit number)
25161215641210045814…70323259792353669119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.032 Γ— 10⁹⁢(97-digit number)
50322431282420091629…40646519584707338239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.006 Γ— 10⁹⁷(98-digit number)
10064486256484018325…81293039169414676479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.012 Γ— 10⁹⁷(98-digit number)
20128972512968036651…62586078338829352959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.025 Γ— 10⁹⁷(98-digit number)
40257945025936073303…25172156677658705919
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.051 Γ— 10⁹⁷(98-digit number)
80515890051872146607…50344313355317411839
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.610 Γ— 10⁹⁸(99-digit number)
16103178010374429321…00688626710634823679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.220 Γ— 10⁹⁸(99-digit number)
32206356020748858642…01377253421269647359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.441 Γ— 10⁹⁸(99-digit number)
64412712041497717285…02754506842539294719
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 1476157

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 84a11246a50d89285943f2912f0d201c4a8050d85d27a6257f71e6a481ea8a1a

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 #1,476,157 on Chainz β†—
Circulating Supply:57,979,520 XPMΒ·at block #6,841,892 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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