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Block #557,902

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 5/23/2014, 6:17:09 AM Β· Difficulty 10.9631 Β· 6,269,127 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e86bcc59cd4a49f8c3a738232df6ead0ddd87b0b73c5f4a1018d454575aa6458
View on Chainz β†—

Height

#557,902

Difficulty

10.963093

Transactions

1

Size

207 B

Version

2

Bits

0af68d46

Nonce

55,007,075

Timestamp

5/23/2014, 6:17:09 AM

Confirmations

6,269,127

Merkle Root

cb90613e3915c2753c8a2700b288073ba45f1ef4606bda07e5cfcb21e00a31ae
Transactions (1)
Coinbasecb90613e3915c2…cfcb21e00a31ae
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

2.976 Γ— 10⁹⁷(98-digit number)
29768668628338954135…46321908437031743600
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
2.976 Γ— 10⁹⁷(98-digit number)
29768668628338954135…46321908437031743601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.953 Γ— 10⁹⁷(98-digit number)
59537337256677908270…92643816874063487201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.190 Γ— 10⁹⁸(99-digit number)
11907467451335581654…85287633748126974401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.381 Γ— 10⁹⁸(99-digit number)
23814934902671163308…70575267496253948801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.762 Γ— 10⁹⁸(99-digit number)
47629869805342326616…41150534992507897601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.525 Γ— 10⁹⁸(99-digit number)
95259739610684653232…82301069985015795201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.905 Γ— 10⁹⁹(100-digit number)
19051947922136930646…64602139970031590401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.810 Γ— 10⁹⁹(100-digit number)
38103895844273861293…29204279940063180801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.620 Γ— 10⁹⁹(100-digit number)
76207791688547722586…58408559880126361601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.524 Γ— 10¹⁰⁰(101-digit number)
15241558337709544517…16817119760252723201
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 557902

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 e86bcc59cd4a49f8c3a738232df6ead0ddd87b0b73c5f4a1018d454575aa6458

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 #557,902 on Chainz β†—
Circulating Supply:57,860,412 XPMΒ·at block #6,827,028 Β· updates every 60s
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