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Block #302,014

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/9/2013, 1:59:51 PM Β· Difficulty 9.9926 Β· 6,528,485 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1a4485f20fbdfe118f9736cbd234e13e307dc6401a032993b5e8a31979b3146e
View on Chainz β†—

Height

#302,014

Difficulty

9.992585

Transactions

2

Size

1017 B

Version

2

Bits

09fe1a13

Nonce

14,778

Timestamp

12/9/2013, 1:59:51 PM

Confirmations

6,528,485

Merkle Root

c3f961253d62277b5d7190dcecb0c56c8013904e925c254697d7c8f2e9811a40
Transactions (2)
Coinbase02c3b0e7985378…326fb6aae0f078
1 in β†’ 1 out10.0100 XPM109 B
AJR5tpKW…J8b618SM
4e6718c674a47b…00da6e33950f0f
5 in β†’ 2 out15.1807 XPM820 B
AJqgy1rr…X1RWu1FfAJcwV1NY…ZkR5KYyi
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.

2.758 Γ— 10⁸⁹(90-digit number)
27589602699233574795…90002695824500520720
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
2.758 Γ— 10⁸⁹(90-digit number)
27589602699233574795…90002695824500520719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.758 Γ— 10⁸⁹(90-digit number)
27589602699233574795…90002695824500520721
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
5.517 Γ— 10⁸⁹(90-digit number)
55179205398467149590…80005391649001041439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.517 Γ— 10⁸⁹(90-digit number)
55179205398467149590…80005391649001041441
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
1.103 Γ— 10⁹⁰(91-digit number)
11035841079693429918…60010783298002082879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.103 Γ— 10⁹⁰(91-digit number)
11035841079693429918…60010783298002082881
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
2.207 Γ— 10⁹⁰(91-digit number)
22071682159386859836…20021566596004165759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.207 Γ— 10⁹⁰(91-digit number)
22071682159386859836…20021566596004165761
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
4.414 Γ— 10⁹⁰(91-digit number)
44143364318773719672…40043133192008331519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.414 Γ— 10⁹⁰(91-digit number)
44143364318773719672…40043133192008331521
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 302014

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 1a4485f20fbdfe118f9736cbd234e13e307dc6401a032993b5e8a31979b3146e

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 #302,014 on Chainz β†—
Circulating Supply:57,888,241 XPMΒ·at block #6,830,498 Β· updates every 60s
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