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Block #454,736

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/22/2014, 3:51:08 AM Β· Difficulty 10.3968 Β· 6,387,857 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5460581df9715d0185d4b6e0b709ebccb07fff3d95cf09912baaa54ea1c979b4
View on Chainz β†—

Height

#454,736

Difficulty

10.396803

Transactions

2

Size

426 B

Version

2

Bits

0a6594e4

Nonce

7,961,276

Timestamp

3/22/2014, 3:51:08 AM

Confirmations

6,387,857

Merkle Root

23b93732d50d9170699710f53845e85f7675caf60aabb90232d36a48da8dacaa
Transactions (2)
Coinbase8c8a911ecf5e8f…371db287faf5a9
1 in β†’ 1 out9.2500 XPM109 B
Ab9QUb4R…JNmsMJJP
deecb09a0370a1…13cb6052c39620
1 in β†’ 2 out1.2011 XPM226 B
ASSfL3vT…5NBonpZWAPzc8gwW…no9eFbfb
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.

1.034 Γ— 10⁹⁷(98-digit number)
10341883701487717134…59925022786867445760
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
1.034 Γ— 10⁹⁷(98-digit number)
10341883701487717134…59925022786867445759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.068 Γ— 10⁹⁷(98-digit number)
20683767402975434269…19850045573734891519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.136 Γ— 10⁹⁷(98-digit number)
41367534805950868539…39700091147469783039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.273 Γ— 10⁹⁷(98-digit number)
82735069611901737079…79400182294939566079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.654 Γ— 10⁹⁸(99-digit number)
16547013922380347415…58800364589879132159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.309 Γ— 10⁹⁸(99-digit number)
33094027844760694831…17600729179758264319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
6.618 Γ— 10⁹⁸(99-digit number)
66188055689521389663…35201458359516528639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.323 Γ— 10⁹⁹(100-digit number)
13237611137904277932…70402916719033057279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.647 Γ— 10⁹⁹(100-digit number)
26475222275808555865…40805833438066114559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.295 Γ— 10⁹⁹(100-digit number)
52950444551617111730…81611666876132229119
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 454736

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 5460581df9715d0185d4b6e0b709ebccb07fff3d95cf09912baaa54ea1c979b4

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 #454,736 on Chainz β†—
Circulating Supply:57,985,174 XPMΒ·at block #6,842,592 Β· updates every 60s
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