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Home/Chain Registry/Block #1,713,907

Block #1,713,907

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 8/12/2016, 2:47:21 PM Β· Difficulty 10.6529 Β· 5,123,270 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c15a4ff95e6f596e561294a2662bd33b01742416a7083876b8a381ec4e702c32
View on Chainz β†—

Difficulty

10.652855

Transactions

1

Size

199 B

Version

2

Bits

0aa72186

Nonce

35,889,101

Timestamp

8/12/2016, 2:47:21 PM

Confirmations

5,123,270

Merkle Root

4eba95d29c9d4f81e7905f049ef2740e971a751e47dba1dc908fb1d1ebd41833
Transactions (1)
Coinbase4eba95d29c9d4f…8fb1d1ebd41833
1 in β†’ 1 out8.8000 XPM109 B
ANUggjHc…x2r3gYjG
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.

2.514 Γ— 10⁹⁴(95-digit number)
25141494767154273303…16023023011593668340
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
2.514 Γ— 10⁹⁴(95-digit number)
25141494767154273303…16023023011593668339
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
5.028 Γ— 10⁹⁴(95-digit number)
50282989534308546606…32046046023187336679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.005 Γ— 10⁹⁡(96-digit number)
10056597906861709321…64092092046374673359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
2.011 Γ— 10⁹⁡(96-digit number)
20113195813723418642…28184184092749346719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
4.022 Γ— 10⁹⁡(96-digit number)
40226391627446837284…56368368185498693439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
8.045 Γ— 10⁹⁡(96-digit number)
80452783254893674569…12736736370997386879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.609 Γ— 10⁹⁢(97-digit number)
16090556650978734913…25473472741994773759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
3.218 Γ— 10⁹⁢(97-digit number)
32181113301957469827…50946945483989547519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
6.436 Γ— 10⁹⁢(97-digit number)
64362226603914939655…01893890967979095039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.287 Γ— 10⁹⁷(98-digit number)
12872445320782987931…03787781935958190079
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 1713907

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 c15a4ff95e6f596e561294a2662bd33b01742416a7083876b8a381ec4e702c32

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 #1,713,907 on Chainz β†—
Circulating Supply:57,941,731 XPMΒ·at block #6,837,176 Β· updates every 60s
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