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Home/Chain Registry/Block #1,416,130

Block #1,416,130

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/16/2016, 7:29:29 PM Β· Difficulty 10.7970 Β· 5,415,552 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
35df6d51b8556e56934665ef2ac7ee2db94bc59124c0413cb9b4fb0c626b8d81
View on Chainz β†—

Difficulty

10.797039

Transactions

2

Size

2.44 KB

Version

2

Bits

0acc0aba

Nonce

252,534,554

Timestamp

1/16/2016, 7:29:29 PM

Confirmations

5,415,552

Merkle Root

571da82851867c82b7a1e0caedfe0bd545ac7af2511951769c002e83829a9262
Transactions (2)
Coinbase95e9e81723c295…d90e6c9e1deb40
1 in β†’ 1 out8.5900 XPM109 B
ARYK3ZuD…dPzJv4ds
7b48af474dbcda…bfdf6d4c4e5c39
15 in β†’ 2 out114.2739 XPM2.25 KB
ASt3fhyk…kB2zqnKhAeB2jkTF…6RUdZ9Cj
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.

2.944 Γ— 10⁹⁴(95-digit number)
29449232698619812393…95856722990965318400
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
2.944 Γ— 10⁹⁴(95-digit number)
29449232698619812393…95856722990965318399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.944 Γ— 10⁹⁴(95-digit number)
29449232698619812393…95856722990965318401
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
5.889 Γ— 10⁹⁴(95-digit number)
58898465397239624786…91713445981930636799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.889 Γ— 10⁹⁴(95-digit number)
58898465397239624786…91713445981930636801
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
1.177 Γ— 10⁹⁡(96-digit number)
11779693079447924957…83426891963861273599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.177 Γ— 10⁹⁡(96-digit number)
11779693079447924957…83426891963861273601
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
2.355 Γ— 10⁹⁡(96-digit number)
23559386158895849914…66853783927722547199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.355 Γ— 10⁹⁡(96-digit number)
23559386158895849914…66853783927722547201
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
4.711 Γ— 10⁹⁡(96-digit number)
47118772317791699829…33707567855445094399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.711 Γ— 10⁹⁡(96-digit number)
47118772317791699829…33707567855445094401
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 1416130

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 35df6d51b8556e56934665ef2ac7ee2db94bc59124c0413cb9b4fb0c626b8d81

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 #1,416,130 on Chainz β†—
Circulating Supply:57,897,562 XPMΒ·at block #6,831,681 Β· updates every 60s
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