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Home/Chain Registry/Block #1,420,016

Block #1,420,016

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/19/2016, 3:08:57 PM Β· Difficulty 10.7900 Β· 5,416,683 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5b404821ad55bc3aa0190afa612b57366b5986dee4d1135ee3ef9d484e76a8c0
View on Chainz β†—

Difficulty

10.789984

Transactions

1

Size

200 B

Version

2

Bits

0aca3c5d

Nonce

1,875,716,767

Timestamp

1/19/2016, 3:08:57 PM

Confirmations

5,416,683

Merkle Root

8673dc0349e9c3bf9c8236f7de866c8d9af891f986f832975090deedd6852b37
Transactions (1)
Coinbase8673dc0349e9c3…90deedd6852b37
1 in β†’ 1 out8.5800 XPM109 B
AZByGyme…gjZvZxX2
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.

3.989 Γ— 10⁹⁢(97-digit number)
39894265732590191067…18805034321208084480
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
3.989 Γ— 10⁹⁢(97-digit number)
39894265732590191067…18805034321208084479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.989 Γ— 10⁹⁢(97-digit number)
39894265732590191067…18805034321208084481
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
7.978 Γ— 10⁹⁢(97-digit number)
79788531465180382135…37610068642416168959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.978 Γ— 10⁹⁢(97-digit number)
79788531465180382135…37610068642416168961
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
1.595 Γ— 10⁹⁷(98-digit number)
15957706293036076427…75220137284832337919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.595 Γ— 10⁹⁷(98-digit number)
15957706293036076427…75220137284832337921
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
3.191 Γ— 10⁹⁷(98-digit number)
31915412586072152854…50440274569664675839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.191 Γ— 10⁹⁷(98-digit number)
31915412586072152854…50440274569664675841
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
6.383 Γ— 10⁹⁷(98-digit number)
63830825172144305708…00880549139329351679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.383 Γ— 10⁹⁷(98-digit number)
63830825172144305708…00880549139329351681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.276 Γ— 10⁹⁸(99-digit number)
12766165034428861141…01761098278658703359
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11
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 1420016

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 5b404821ad55bc3aa0190afa612b57366b5986dee4d1135ee3ef9d484e76a8c0

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 #1,420,016 on Chainz β†—
Circulating Supply:57,937,873 XPMΒ·at block #6,836,698 Β· updates every 60s
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