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Block #61,884

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/18/2013, 3:53:05 PM Β· Difficulty 8.9746 Β· 6,742,151 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
454a7270ba2e26dac4312befc971295d97665e38754fe4e95b455f79620efdaf
View on Chainz β†—

Height

#61,884

Difficulty

8.974649

Transactions

1

Size

199 B

Version

2

Bits

08f98299

Nonce

190

Timestamp

7/18/2013, 3:53:05 PM

Confirmations

6,742,151

Merkle Root

c6adee55fe57c7d5ee22e26d7977b45fc444cd80b0fbc27049f6e8c78cdb7d1b
Transactions (1)
Coinbasec6adee55fe57c7…f6e8c78cdb7d1b
1 in β†’ 1 out12.4000 XPM110 B
AKsLKPc8…zkBgUqcr
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.

1.342 Γ— 10⁹²(93-digit number)
13420944026803440486…05872536270641100400
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
1.342 Γ— 10⁹²(93-digit number)
13420944026803440486…05872536270641100399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.342 Γ— 10⁹²(93-digit number)
13420944026803440486…05872536270641100401
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
2.684 Γ— 10⁹²(93-digit number)
26841888053606880972…11745072541282200799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.684 Γ— 10⁹²(93-digit number)
26841888053606880972…11745072541282200801
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
5.368 Γ— 10⁹²(93-digit number)
53683776107213761944…23490145082564401599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.368 Γ— 10⁹²(93-digit number)
53683776107213761944…23490145082564401601
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
1.073 Γ— 10⁹³(94-digit number)
10736755221442752388…46980290165128803199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.073 Γ— 10⁹³(94-digit number)
10736755221442752388…46980290165128803201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8
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 61884

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 454a7270ba2e26dac4312befc971295d97665e38754fe4e95b455f79620efdaf

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 #61,884 on Chainz β†—
Circulating Supply:57,676,332 XPMΒ·at block #6,804,034 Β· updates every 60s
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