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Block #1,337,816

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/23/2015, 9:03:22 AM Β· Difficulty 10.7966 Β· 5,467,494 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a2cd15712a8efc52f1330d590b173cea1ca517d3590ea5fb3728e80e39b85a44
View on Chainz β†—

Difficulty

10.796635

Transactions

1

Size

199 B

Version

2

Bits

0acbf040

Nonce

1,381,713,481

Timestamp

11/23/2015, 9:03:22 AM

Confirmations

5,467,494

Merkle Root

aa0410d44b0366b51df87ded7607eca361953472ecbedb7707bd371b446b1b8b
Transactions (1)
Coinbaseaa0410d44b0366…bd371b446b1b8b
1 in β†’ 1 out8.5700 XPM109 B
AG7z4Pce…9NwZwgdz
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.

4.698 Γ— 10⁹⁡(96-digit number)
46989998645929479001…73892296235644600320
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
4.698 Γ— 10⁹⁡(96-digit number)
46989998645929479001…73892296235644600319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.698 Γ— 10⁹⁡(96-digit number)
46989998645929479001…73892296235644600321
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
9.397 Γ— 10⁹⁡(96-digit number)
93979997291858958002…47784592471289200639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.397 Γ— 10⁹⁡(96-digit number)
93979997291858958002…47784592471289200641
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
1.879 Γ— 10⁹⁢(97-digit number)
18795999458371791600…95569184942578401279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.879 Γ— 10⁹⁢(97-digit number)
18795999458371791600…95569184942578401281
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
3.759 Γ— 10⁹⁢(97-digit number)
37591998916743583200…91138369885156802559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.759 Γ— 10⁹⁢(97-digit number)
37591998916743583200…91138369885156802561
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
7.518 Γ— 10⁹⁢(97-digit number)
75183997833487166401…82276739770313605119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.518 Γ— 10⁹⁢(97-digit number)
75183997833487166401…82276739770313605121
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 1337816

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 a2cd15712a8efc52f1330d590b173cea1ca517d3590ea5fb3728e80e39b85a44

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 #1,337,816 on Chainz β†—
Circulating Supply:57,686,557 XPMΒ·at block #6,805,309 Β· updates every 60s
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