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Home/Chain Registry/Block #2,880,992

Block #2,880,992

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 10/14/2018, 5:18:39 PM Β· Difficulty 11.6296 Β· 3,958,393 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4086a8aacf263010342cc178557fa736b1a9468bcad85861bb247b892d67401b
View on Chainz β†—

Difficulty

11.629602

Transactions

1

Size

199 B

Version

2

Bits

0ba12d9b

Nonce

1,815,655,746

Timestamp

10/14/2018, 5:18:39 PM

Confirmations

3,958,393

Merkle Root

58d7493c79cee39a22534afc36824dd00f84930a5a0e69bffa97be1efb5ebd85
Transactions (1)
Coinbase58d7493c79cee3…97be1efb5ebd85
1 in β†’ 1 out7.3800 XPM110 B
Abt1wZSZ…aqyQpQGi
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.

2.857 Γ— 10⁹¹(92-digit number)
28579905204779488970…82047804345732333640
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
2.857 Γ— 10⁹¹(92-digit number)
28579905204779488970…82047804345732333639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.857 Γ— 10⁹¹(92-digit number)
28579905204779488970…82047804345732333641
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
5.715 Γ— 10⁹¹(92-digit number)
57159810409558977940…64095608691464667279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.715 Γ— 10⁹¹(92-digit number)
57159810409558977940…64095608691464667281
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
1.143 Γ— 10⁹²(93-digit number)
11431962081911795588…28191217382929334559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.143 Γ— 10⁹²(93-digit number)
11431962081911795588…28191217382929334561
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
2.286 Γ— 10⁹²(93-digit number)
22863924163823591176…56382434765858669119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.286 Γ— 10⁹²(93-digit number)
22863924163823591176…56382434765858669121
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
4.572 Γ— 10⁹²(93-digit number)
45727848327647182352…12764869531717338239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.572 Γ— 10⁹²(93-digit number)
45727848327647182352…12764869531717338241
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
9.145 Γ— 10⁹²(93-digit number)
91455696655294364704…25529739063434676479
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 2880992

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 4086a8aacf263010342cc178557fa736b1a9468bcad85861bb247b892d67401b

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 #2,880,992 on Chainz β†—
Circulating Supply:57,959,363 XPMΒ·at block #6,839,384 Β· updates every 60s
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