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Home/Chain Registry/Block #1,412,137

Block #1,412,137

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/13/2016, 9:55:17 PM Β· Difficulty 10.8040 Β· 5,433,517 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
07c298290137627a05b5d71f43ca006c49c1888425f7253d9b560541a956d379
View on Chainz β†—

Difficulty

10.804022

Transactions

1

Size

199 B

Version

2

Bits

0acdd468

Nonce

1,487,580,250

Timestamp

1/13/2016, 9:55:17 PM

Confirmations

5,433,517

Merkle Root

c3be323198bbd78632be2c594836832f89a6c10db96093c439751c8d488ff563
Transactions (1)
Coinbasec3be323198bbd7…751c8d488ff563
1 in β†’ 1 out8.5500 XPM110 B
AGAW6B9p…637Hx7Sz
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.

1.222 Γ— 10⁹²(93-digit number)
12220620955294377875…00751727564651710640
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
1.222 Γ— 10⁹²(93-digit number)
12220620955294377875…00751727564651710639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.222 Γ— 10⁹²(93-digit number)
12220620955294377875…00751727564651710641
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
2.444 Γ— 10⁹²(93-digit number)
24441241910588755750…01503455129303421279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.444 Γ— 10⁹²(93-digit number)
24441241910588755750…01503455129303421281
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
4.888 Γ— 10⁹²(93-digit number)
48882483821177511501…03006910258606842559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.888 Γ— 10⁹²(93-digit number)
48882483821177511501…03006910258606842561
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
9.776 Γ— 10⁹²(93-digit number)
97764967642355023003…06013820517213685119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.776 Γ— 10⁹²(93-digit number)
97764967642355023003…06013820517213685121
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
1.955 Γ— 10⁹³(94-digit number)
19552993528471004600…12027641034427370239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.955 Γ— 10⁹³(94-digit number)
19552993528471004600…12027641034427370241
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
3.910 Γ— 10⁹³(94-digit number)
39105987056942009201…24055282068854740479
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 1412137

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 07c298290137627a05b5d71f43ca006c49c1888425f7253d9b560541a956d379

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 #1,412,137 on Chainz β†—
Circulating Supply:58,009,680 XPMΒ·at block #6,845,653 Β· updates every 60s
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