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Home/Chain Registry/Block #3,055,894

Block #3,055,894

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/16/2019, 9:04:19 PM Β· Difficulty 11.0084 Β· 3,770,662 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7cbfa915409b8602c9f2ffd7f4e666dd0b9715abba13902a8594bb81cd87790b
View on Chainz β†—

Difficulty

11.008414

Transactions

1

Size

200 B

Version

2

Bits

0b02276e

Nonce

94,886,614

Timestamp

2/16/2019, 9:04:19 PM

Confirmations

3,770,662

Merkle Root

8c62af1d5c48e0a768e51879b9cda37403b6f8194349fb1c0e3dfcbe102b579c
Transactions (1)
Coinbase8c62af1d5c48e0…3dfcbe102b579c
1 in β†’ 1 out8.2400 XPM109 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.

2.038 Γ— 10⁹⁷(98-digit number)
20380043771427753039…33976236317386342400
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
2.038 Γ— 10⁹⁷(98-digit number)
20380043771427753039…33976236317386342399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.038 Γ— 10⁹⁷(98-digit number)
20380043771427753039…33976236317386342401
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
4.076 Γ— 10⁹⁷(98-digit number)
40760087542855506079…67952472634772684799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.076 Γ— 10⁹⁷(98-digit number)
40760087542855506079…67952472634772684801
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
8.152 Γ— 10⁹⁷(98-digit number)
81520175085711012159…35904945269545369599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.152 Γ— 10⁹⁷(98-digit number)
81520175085711012159…35904945269545369601
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
1.630 Γ— 10⁹⁸(99-digit number)
16304035017142202431…71809890539090739199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.630 Γ— 10⁹⁸(99-digit number)
16304035017142202431…71809890539090739201
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
3.260 Γ— 10⁹⁸(99-digit number)
32608070034284404863…43619781078181478399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.260 Γ— 10⁹⁸(99-digit number)
32608070034284404863…43619781078181478401
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
6.521 Γ— 10⁹⁸(99-digit number)
65216140068568809727…87239562156362956799
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 3055894

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 7cbfa915409b8602c9f2ffd7f4e666dd0b9715abba13902a8594bb81cd87790b

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 #3,055,894 on Chainz β†—
Circulating Supply:57,856,599 XPMΒ·at block #6,826,555 Β· updates every 60s
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