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Block #248,201

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/7/2013, 6:00:03 AM Β· Difficulty 9.9655 Β· 6,551,980 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
67dc57b25de8e4cc5fb1dda56386b4e20fbaf4f0f616e9cf1fc9695b0a77179b
View on Chainz β†—

Height

#248,201

Difficulty

9.965483

Transactions

2

Size

426 B

Version

2

Bits

09f729e2

Nonce

116,763

Timestamp

11/7/2013, 6:00:03 AM

Confirmations

6,551,980

Merkle Root

d209beb486f5ace0050c45c0c20afd8a08646d8ab53f7981aae55adcda52c93f
Transactions (2)
Coinbasee40f7ac488da14…46ba344ae91cfc
1 in β†’ 1 out10.0600 XPM109 B
AdhZ2T8w…K41cgqtZ
77cd61f021b021…6cbdd59bc80782
1 in β†’ 2 out10.0500 XPM227 B
ANmGQNfJ…HxcmxbWJAb1iqm2d…G7ZsrgRJ
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.

1.080 Γ— 10⁹⁴(95-digit number)
10809951394217202601…18835610971066419200
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
1.080 Γ— 10⁹⁴(95-digit number)
10809951394217202601…18835610971066419199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.080 Γ— 10⁹⁴(95-digit number)
10809951394217202601…18835610971066419201
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
2.161 Γ— 10⁹⁴(95-digit number)
21619902788434405203…37671221942132838399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.161 Γ— 10⁹⁴(95-digit number)
21619902788434405203…37671221942132838401
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
4.323 Γ— 10⁹⁴(95-digit number)
43239805576868810406…75342443884265676799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.323 Γ— 10⁹⁴(95-digit number)
43239805576868810406…75342443884265676801
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
8.647 Γ— 10⁹⁴(95-digit number)
86479611153737620812…50684887768531353599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.647 Γ— 10⁹⁴(95-digit number)
86479611153737620812…50684887768531353601
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
1.729 Γ— 10⁹⁡(96-digit number)
17295922230747524162…01369775537062707199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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 9
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 248201

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 67dc57b25de8e4cc5fb1dda56386b4e20fbaf4f0f616e9cf1fc9695b0a77179b

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 #248,201 on Chainz β†—
Circulating Supply:57,645,517 XPMΒ·at block #6,800,180 Β· updates every 60s
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