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Home/Chain Registry/Block #2,455,732

Block #2,455,732

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/3/2018, 12:55:30 PM Β· Difficulty 10.9531 Β· 4,385,997 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f1c4850c2ca2127eb6f7ab8dfb062ce808e5ca1c7640f07eb70dd73f83a84ce4
View on Chainz β†—

Difficulty

10.953095

Transactions

1

Size

200 B

Version

2

Bits

0af3fe02

Nonce

2,086,881,522

Timestamp

1/3/2018, 12:55:30 PM

Confirmations

4,385,997

Merkle Root

962c456a469cf3e84f17c42729ca2907b007e82f33495bf557c39ffd3649de73
Transactions (1)
Coinbase962c456a469cf3…c39ffd3649de73
1 in β†’ 1 out8.3200 XPM110 B
ASNasbZ5…qaFMKUqH
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.

1.546 Γ— 10⁹⁴(95-digit number)
15469609727154133202…36444658290782647280
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
1.546 Γ— 10⁹⁴(95-digit number)
15469609727154133202…36444658290782647279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.546 Γ— 10⁹⁴(95-digit number)
15469609727154133202…36444658290782647281
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
3.093 Γ— 10⁹⁴(95-digit number)
30939219454308266405…72889316581565294559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.093 Γ— 10⁹⁴(95-digit number)
30939219454308266405…72889316581565294561
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
6.187 Γ— 10⁹⁴(95-digit number)
61878438908616532810…45778633163130589119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.187 Γ— 10⁹⁴(95-digit number)
61878438908616532810…45778633163130589121
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
1.237 Γ— 10⁹⁡(96-digit number)
12375687781723306562…91557266326261178239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.237 Γ— 10⁹⁡(96-digit number)
12375687781723306562…91557266326261178241
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
2.475 Γ— 10⁹⁡(96-digit number)
24751375563446613124…83114532652522356479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.475 Γ— 10⁹⁡(96-digit number)
24751375563446613124…83114532652522356481
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 2455732

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 f1c4850c2ca2127eb6f7ab8dfb062ce808e5ca1c7640f07eb70dd73f83a84ce4

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 #2,455,732 on Chainz β†—
Circulating Supply:57,978,213 XPMΒ·at block #6,841,728 Β· updates every 60s
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