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Block #880,804

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 1/3/2015, 5:57:23 PM Β· Difficulty 10.9614 Β· 5,945,825 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fbfdab24ae75dbc119e280ff8834d2fb8ed0211cc07b1a064810494669fb145d
View on Chainz β†—

Height

#880,804

Difficulty

10.961365

Transactions

1

Size

207 B

Version

2

Bits

0af61c06

Nonce

1,550,840,067

Timestamp

1/3/2015, 5:57:23 PM

Confirmations

5,945,825

Merkle Root

7329dc1d5efd568bb9af9736979d8d9cf729ac2b96e62b2a8605f03231ced3e9
Transactions (1)
Coinbase7329dc1d5efd56…05f03231ced3e9
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
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.

1.323 Γ— 10⁹⁸(99-digit number)
13237021682881535143…87460816453206876160
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
1.323 Γ— 10⁹⁸(99-digit number)
13237021682881535143…87460816453206876159
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.323 Γ— 10⁹⁸(99-digit number)
13237021682881535143…87460816453206876161
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
2.647 Γ— 10⁹⁸(99-digit number)
26474043365763070287…74921632906413752319
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.647 Γ— 10⁹⁸(99-digit number)
26474043365763070287…74921632906413752321
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
5.294 Γ— 10⁹⁸(99-digit number)
52948086731526140575…49843265812827504639
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.294 Γ— 10⁹⁸(99-digit number)
52948086731526140575…49843265812827504641
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
1.058 Γ— 10⁹⁹(100-digit number)
10589617346305228115…99686531625655009279
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.058 Γ— 10⁹⁹(100-digit number)
10589617346305228115…99686531625655009281
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
2.117 Γ— 10⁹⁹(100-digit number)
21179234692610456230…99373063251310018559
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.117 Γ— 10⁹⁹(100-digit number)
21179234692610456230…99373063251310018561
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
4.235 Γ— 10⁹⁹(100-digit number)
42358469385220912460…98746126502620037119
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 880804

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 fbfdab24ae75dbc119e280ff8834d2fb8ed0211cc07b1a064810494669fb145d

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 #880,804 on Chainz β†—
Circulating Supply:57,857,177 XPMΒ·at block #6,826,628 Β· updates every 60s
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