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Home/Chain Registry/Block #1,715,460

Block #1,715,460

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/13/2016, 3:30:03 PM Β· Difficulty 10.6577 Β· 5,117,200 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
462ff78b87d94b3b6b0c15b8575fae2e0d0f3f44c8d11f2669a879d3f4113f86
View on Chainz β†—

Difficulty

10.657692

Transactions

1

Size

242 B

Version

2

Bits

0aa85e87

Nonce

597,161,426

Timestamp

8/13/2016, 3:30:03 PM

Confirmations

5,117,200

Merkle Root

c087c9b56f5dba4146aa2af3c0df5649eb02c78efed4187435ec55b5383e279b
Transactions (1)
Coinbasec087c9b56f5dba…ec55b5383e279b
1 in β†’ 2 out8.7900 XPM152 B
ARf92pmr…CsyVkynHALPu3s2c…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.

2.444 Γ— 10⁹⁡(96-digit number)
24447271897784287304…50441360320048722560
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 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.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
2.444 Γ— 10⁹⁡(96-digit number)
24447271897784287304…50441360320048722559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.444 Γ— 10⁹⁡(96-digit number)
24447271897784287304…50441360320048722561
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
4.889 Γ— 10⁹⁡(96-digit number)
48894543795568574609…00882720640097445119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.889 Γ— 10⁹⁡(96-digit number)
48894543795568574609…00882720640097445121
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
9.778 Γ— 10⁹⁡(96-digit number)
97789087591137149218…01765441280194890239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.778 Γ— 10⁹⁡(96-digit number)
97789087591137149218…01765441280194890241
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
1.955 Γ— 10⁹⁢(97-digit number)
19557817518227429843…03530882560389780479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.955 Γ— 10⁹⁢(97-digit number)
19557817518227429843…03530882560389780481
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
3.911 Γ— 10⁹⁢(97-digit number)
39115635036454859687…07061765120779560959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.911 Γ— 10⁹⁢(97-digit number)
39115635036454859687…07061765120779560961
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. 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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 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 1715460

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 462ff78b87d94b3b6b0c15b8575fae2e0d0f3f44c8d11f2669a879d3f4113f86

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 #1,715,460 on Chainz β†—
Circulating Supply:57,905,432 XPMΒ·at block #6,832,659 Β· updates every 60s
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