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Block #306,479

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/12/2013, 1:53:17 AM Β· Difficulty 9.9939 Β· 6,499,598 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4d702301a46a0dcde66d6780dace7597b1f9d7e79c872d1c9329333ffc806701
View on Chainz β†—

Height

#306,479

Difficulty

9.993898

Transactions

2

Size

720 B

Version

2

Bits

09fe7013

Nonce

130,573

Timestamp

12/12/2013, 1:53:17 AM

Confirmations

6,499,598

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

ace13bb2cf043dd2df266ffc8348b85dea77ba1bfc370a1312f577c08722b22a
Transactions (2)
Coinbase25409c54388f87…7a8da998912509
1 in β†’ 1 out10.0100 XPM110 B
AeKNrjNj…1NEq95Ta
5bb03c98eb02b7…d98e2c4ff75cc5
3 in β†’ 2 out3.0833 XPM522 B
Ad5d1JE4…B2pqmrvUAa73duv4…t6J7F71e
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.

1.240 Γ— 10⁹⁰(91-digit number)
12400942284162833683…11208073318095892529
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
1.240 Γ— 10⁹⁰(91-digit number)
12400942284162833683…11208073318095892529
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.240 Γ— 10⁹⁰(91-digit number)
12400942284162833683…11208073318095892531
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
2.480 Γ— 10⁹⁰(91-digit number)
24801884568325667366…22416146636191785059
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.480 Γ— 10⁹⁰(91-digit number)
24801884568325667366…22416146636191785061
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
4.960 Γ— 10⁹⁰(91-digit number)
49603769136651334732…44832293272383570119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.960 Γ— 10⁹⁰(91-digit number)
49603769136651334732…44832293272383570121
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
9.920 Γ— 10⁹⁰(91-digit number)
99207538273302669464…89664586544767140239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.920 Γ— 10⁹⁰(91-digit number)
99207538273302669464…89664586544767140241
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
1.984 Γ— 10⁹¹(92-digit number)
19841507654660533892…79329173089534280479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.984 Γ— 10⁹¹(92-digit number)
19841507654660533892…79329173089534280481
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.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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
Cross-reference on Chainz Explorer
Circulating Supply:57,692,689 XPMΒ·at block #6,806,076 Β· updates every 60s
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