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Home/Chain Registry/Block #1,880,211

Block #1,880,211

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/5/2016, 6:27:07 PM Β· Difficulty 10.6922 Β· 4,962,765 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
66a7a9a07c282f48fd6226de1d7abdabcce3d2c453af983c5bc4b58ec35d7269
View on Chainz β†—

Difficulty

10.692208

Transactions

1

Size

243 B

Version

2

Bits

0ab13487

Nonce

1,230,674,938

Timestamp

12/5/2016, 6:27:07 PM

Confirmations

4,962,765

Merkle Root

5a96bcf40a6c48146214acc815d916cfd3031aa71ada41920e831988fd959457
Transactions (1)
Coinbase5a96bcf40a6c48…831988fd959457
1 in β†’ 2 out8.7300 XPM152 B
AXpBZ8ks…8zJpe999ALPu3s2c…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.

5.833 Γ— 10⁹⁡(96-digit number)
58338799402979681350…12522983096767033320
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
5.833 Γ— 10⁹⁡(96-digit number)
58338799402979681350…12522983096767033319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.833 Γ— 10⁹⁡(96-digit number)
58338799402979681350…12522983096767033321
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
1.166 Γ— 10⁹⁢(97-digit number)
11667759880595936270…25045966193534066639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.166 Γ— 10⁹⁢(97-digit number)
11667759880595936270…25045966193534066641
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
2.333 Γ— 10⁹⁢(97-digit number)
23335519761191872540…50091932387068133279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.333 Γ— 10⁹⁢(97-digit number)
23335519761191872540…50091932387068133281
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
4.667 Γ— 10⁹⁢(97-digit number)
46671039522383745080…00183864774136266559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.667 Γ— 10⁹⁢(97-digit number)
46671039522383745080…00183864774136266561
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
9.334 Γ— 10⁹⁢(97-digit number)
93342079044767490160…00367729548272533119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.334 Γ— 10⁹⁢(97-digit number)
93342079044767490160…00367729548272533121
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 1880211

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 66a7a9a07c282f48fd6226de1d7abdabcce3d2c453af983c5bc4b58ec35d7269

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 #1,880,211 on Chainz β†—
Circulating Supply:57,988,162 XPMΒ·at block #6,842,975 Β· updates every 60s
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