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Block #309,645

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 12/13/2013, 4:58:45 PM Β· Difficulty 9.9949 Β· 6,496,323 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ecc3a3c132a94fa3408be9d6d2a3fd4998c701c95b0c5c339f3733e4b9d5e993
View on Chainz β†—

Height

#309,645

Difficulty

9.994905

Transactions

1

Size

207 B

Version

2

Bits

09feb219

Nonce

30,594

Timestamp

12/13/2013, 4:58:45 PM

Confirmations

6,496,323

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3211215948039d4d314b5798a2695a3bc02e47f7bb1891dfee81d1d84b0a22fa
Transactions (1)
Coinbase3211215948039d…81d1d84b0a22fa
1 in β†’ 1 out10.0000 XPM116 B
AbwWkWZt…kawDhufa
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.

1.806 Γ— 10⁹⁸(99-digit number)
18066979250915455029…46673811872225991679
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
1.806 Γ— 10⁹⁸(99-digit number)
18066979250915455029…46673811872225991679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.806 Γ— 10⁹⁸(99-digit number)
18066979250915455029…46673811872225991681
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
3.613 Γ— 10⁹⁸(99-digit number)
36133958501830910058…93347623744451983359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.613 Γ— 10⁹⁸(99-digit number)
36133958501830910058…93347623744451983361
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
7.226 Γ— 10⁹⁸(99-digit number)
72267917003661820117…86695247488903966719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.226 Γ— 10⁹⁸(99-digit number)
72267917003661820117…86695247488903966721
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
1.445 Γ— 10⁹⁹(100-digit number)
14453583400732364023…73390494977807933439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.445 Γ— 10⁹⁹(100-digit number)
14453583400732364023…73390494977807933441
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
2.890 Γ— 10⁹⁹(100-digit number)
28907166801464728046…46780989955615866879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.890 Γ— 10⁹⁹(100-digit number)
28907166801464728046…46780989955615866881
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
5.781 Γ— 10⁹⁹(100-digit number)
57814333602929456093…93561979911231733759
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,691,818 XPMΒ·at block #6,805,967 Β· updates every 60s
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