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Home/Chain Registry/Block #1,587,556

Block #1,587,556

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/16/2016, 8:04:53 PM Β· Difficulty 10.6509 Β· 5,254,915 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0997a22830f9e449f2f720b24d2aa4cfd2ccbc2d194fbf3ee5ac09cb0db95e8a
View on Chainz β†—

Difficulty

10.650931

Transactions

1

Size

242 B

Version

2

Bits

0aa6a368

Nonce

1,298,919,642

Timestamp

5/16/2016, 8:04:53 PM

Confirmations

5,254,915

Merkle Root

d6f5bbb488041f83ef78f8727ab17fae44cb076fbcd8c3e53b15fe62edb44b25
Transactions (1)
Coinbased6f5bbb488041f…15fe62edb44b25
1 in β†’ 2 out8.8000 XPM152 B
AJgZBh3x…9DpUcwi5ALPu3s2c…EJXLjVFh
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.

9.802 Γ— 10⁹⁴(95-digit number)
98025332466416418394…04354595077863082960
Discovered Prime Numbers
p_k = 2^k Γ— origin + 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 + 1
9.802 Γ— 10⁹⁴(95-digit number)
98025332466416418394…04354595077863082961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.960 Γ— 10⁹⁡(96-digit number)
19605066493283283678…08709190155726165921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.921 Γ— 10⁹⁡(96-digit number)
39210132986566567357…17418380311452331841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
7.842 Γ— 10⁹⁡(96-digit number)
78420265973133134715…34836760622904663681
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.568 Γ— 10⁹⁢(97-digit number)
15684053194626626943…69673521245809327361
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
3.136 Γ— 10⁹⁢(97-digit number)
31368106389253253886…39347042491618654721
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
6.273 Γ— 10⁹⁢(97-digit number)
62736212778506507772…78694084983237309441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.254 Γ— 10⁹⁷(98-digit number)
12547242555701301554…57388169966474618881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.509 Γ— 10⁹⁷(98-digit number)
25094485111402603108…14776339932949237761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
5.018 Γ— 10⁹⁷(98-digit number)
50188970222805206217…29552679865898475521
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 Second 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 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 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 1587556

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 0997a22830f9e449f2f720b24d2aa4cfd2ccbc2d194fbf3ee5ac09cb0db95e8a

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 #1,587,556 on Chainz β†—
Circulating Supply:57,984,186 XPMΒ·at block #6,842,470 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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