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Home/Chain Registry/Block #2,916,857

Block #2,916,857

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/10/2018, 3:43:59 AM Β· Difficulty 11.4285 Β· 3,928,157 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8fafcbcad5925c1845755c6ceb8588c26eeb24a53aaf1fd1118bee06aa98d7cd
View on Chainz β†—

Difficulty

11.428466

Transactions

1

Size

201 B

Version

2

Bits

0b6daffb

Nonce

1,347,540,436

Timestamp

11/10/2018, 3:43:59 AM

Confirmations

3,928,157

Merkle Root

fb9b16ceb863e36e7be7abe2469af5383565f31e0a78498ca12df576085175c6
Transactions (1)
Coinbasefb9b16ceb863e3…2df576085175c6
1 in β†’ 1 out7.6400 XPM110 B
AUMQRepm…tAfKmdW1
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.

1.708 Γ— 10⁹⁸(99-digit number)
17086774027410214818…23898463848531886080
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
1.708 Γ— 10⁹⁸(99-digit number)
17086774027410214818…23898463848531886079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.708 Γ— 10⁹⁸(99-digit number)
17086774027410214818…23898463848531886081
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
3.417 Γ— 10⁹⁸(99-digit number)
34173548054820429636…47796927697063772159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.417 Γ— 10⁹⁸(99-digit number)
34173548054820429636…47796927697063772161
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
6.834 Γ— 10⁹⁸(99-digit number)
68347096109640859272…95593855394127544319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.834 Γ— 10⁹⁸(99-digit number)
68347096109640859272…95593855394127544321
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
1.366 Γ— 10⁹⁹(100-digit number)
13669419221928171854…91187710788255088639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.366 Γ— 10⁹⁹(100-digit number)
13669419221928171854…91187710788255088641
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
2.733 Γ— 10⁹⁹(100-digit number)
27338838443856343709…82375421576510177279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.733 Γ— 10⁹⁹(100-digit number)
27338838443856343709…82375421576510177281
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
5.467 Γ— 10⁹⁹(100-digit number)
54677676887712687418…64750843153020354559
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 2916857

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 8fafcbcad5925c1845755c6ceb8588c26eeb24a53aaf1fd1118bee06aa98d7cd

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 #2,916,857 on Chainz β†—
Circulating Supply:58,004,534 XPMΒ·at block #6,845,013 Β· updates every 60s
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